Calculate Inductance

How to Calculate the Henrys in a Coil

An inductor is basically just a coil of wire. The inductance of an inductor is a measure of its ability to store energy in the form of a magnetic field; when the current in the coil changes, it follows from Lenz's Law that the magnetic field will induce motion of charges in such a way that it will resist change in the current. The inductance is equal to the electromotive force or EMF per unit of rate of change of current. Inductance is measured using a unit called the Henry or H. Measure the length of the coil of wire in meters or centimeters. It's important to use metric units, since the Henry is based on the metric system. Determine how many turns there are in the coil -- i.e. how many times the wire is coiled. Calculate the cross-sectional area of the wire coil by measuring its radius and plugging this into the formula π*r squared. Calculate the inductance using the following formula: Inductance = µ N² A / length where N is the number of turns in the coil, A is the cross-sectional area of the coil, and length is the length of the coil. µ (or "mu") is a constant called the vacuum permeability constant and has the value 4π x 10^-7 H/m.

How to Calculate Electrical Winding Wires
by Weight & Length

Electrical winding wire is used to create inductors. An inductor is a iron core with coils of wire wrapped around it. The number of turns of the coil wire determines the inductance value. Inductors are used in a variety of electrical devices including transformers and electric motors. In fact, the transformer ratio is the ratio between the primary winding and secondary winding where the word winding refer to coils of wire. For this reason, calculating electrical winding wire is analogous to calculating the value of the inductance associated with the winding. Find the radius of the wire coil or winding in meters. Refer to the manufacturer's specification regarding the winding or measure it with a micrometer from the center of the wire coil to the outer section of the coil. Call this value "r." Find the area of the winding using the formula A = π * r² where π is 3.1415. For example, if r is 1.5 meters: A = 3.1415 * (1.5)(1.5) = 7.068 square meters. Find the number of wire turns and the length of the wire. This is the number of times the wire wraps around the iron core. Refer to manufacturer's specifications of the winding for these values. Call the number of turns N and the length l. Calculate the inductance associated with the winding using the formula L = (u0 * A * N^2)/l where u0 is the permeability of free space at 12.56 x 10^ -7 If N is 100 turns, l is 6 meters and A is 7.069 square meters. L = [(12.56 x 10^-7)(7.069)(100)(100)]/6 = 14.79 mH or millihenries. Note: The combination of the area and the length in the formula takes into account the weight of the wire.

How to Calculate Toroidal Transformers

A toroidal transformer is a transformer shaped like a doughnut. It has a round iron core with a coil of insulated wire wrapped around it. The iron core with the coil of wire is also called the "winding." Once powered, the winding generates a magnetic field and stores energy. The amount of energy is measured in units of inductance. As with most transformers, toroidal transformers have both a primary and secondary inductive winding, which is used to step down or step up the input voltage applied to the primary winding. Determine the number of turns in the primary winding of the transformer. Call this value "N." Refer to the transformer specifications. As an example, assume N is 300 turns. Find the radius of the transformer. Refer to transformer specifications. As an example, assume radius is 0.030 meters. Calculate the area using the formula A = π * r² where π is 3.1415. Continuing with the example: A = 3.1415 * (0.030)(0.030) = 0.0028 square meters Calculate the inductance of the primary winding using the formula L = (μ0 * N² * A) / 2 * π * r, where μ0 is the relative permeability of space with a value of: 4 * π * 10^-7 T m/A. Continuing with the example: μ0 = 4 * π * 10^-7 = 4 * 3.1415 * 10^-7 = 12.56 * 10^-7 L = [(12.56 * 10^-7)(300^2)(0.0028)] / [(2)(3.1415)(0.030)] = 0.000316 / 0 .188 = 0.00168 henries or 1.68 millihenries.

How to Calculate Induced Armature Voltage

An armature is the rotating solenoid inside of DC machines. Engineers use DC machines to build a generator or a motor. When it's used as a generator, a gas turbine or a diesel engine rotates the armature and the armature generates electric power. When it's used as a motor, electric power rotates the armature and the armature generates the mechanical energy needed to operate a motor. In both cases, the armature rotates in a magnetic field to produce the required output. Find the total number of conductors on the armature, or "Z." Refer to the armature design specifications. Find the speed of rotation of the armature, or "N," in revolutions per minute or rpms. Refer to the armature design specifications. Find the magnetic flux per pole on the armature, or "M," in units of Webers. Refer to the armature design specifications. Calculate the induced armature voltage using the formula: Eo = (Z N M)/ 60 where Eo is the induced armature voltage. For example, if Z is 360 conductors, N is 1200 rpm and M is 0.04 Wb, then [(360)(1200)(0.04)]/60 equals 288 volts.

How to Calculate the Inductance of a Coil

Coils are inductors–they resist the flow of alternating current. This inductance is accomplished by magnetically shifting the relationship between the voltage (how much electromagnetic force is being applied) and the current (how many electrons are flowing). Usually voltage and current are in phase–both high at the same time, both low at the same time. Coils change that, and the stronger the coil (the more henrys, or units of inductance), the bigger the phase shift. Calculate the inductance of a coil as an educational exercise or if you expect someday to build a radio from spare parts. The coils you buy will have the henrys (measure of inductance) clearly marked. Knowing the formula will help you understand the behavior of coils, and there is no better way to understand and remember a formula than to use it. Take two measurements: the length of the coil ('L') and the diameter of the coil ('D'). The more accurately you make these measurements, the more accurate your results will be. In the calculation that follows, "L" will be the length of the coil and "D" will be the diameter of the coil. Now count the number of rings in the coil. This will be "N" in the formula. Now that you have values for L, D and N, you can do the calculation. Compute the inductance by squaring both N and D. Then multiply the squares and divide the result by (18D + 40L). This will give you the inductance in microhenrys. There are one million microhenrys in a henry. The formula is: The micro henrys of inductance in a coil: L = (N²)(D²)/(18D + 40L) where "N" equals the number of rings in the coil, "D" equals the diameter of the coil and "L" equals the length of the coil. Unless your wires are insulated, your calculation will be incorrect if any of the rings are touching This formula can change if you are using an unusual gauge of wire or a core for the coil. Some online calculators can take this into consideration

What Is Ohm's Law & What Does It Tell Us?

George Ohm published the formula for Ohm’s Law in 1827. Ohm’s Law states that the electric current that passes through a conductor is in direct proportion with the potential difference across it. In other words, the constant proportionality results in the resistance of the conductor. Ohm’s Law states that the direct current that flows in the conductor is also directly proportional to the difference between its ends. Ohm’s Law is formulated as E = IR , where E is the voltage (EMF), I is the current and R is the resistance of the conductor. Ohm’s Law represents the most important mathematical relationship between voltage, resistance and current.

Current (I = E/R) According to Ohm’s Law, current flows on a wire conductor like water flows down a river. On the surface of a conductor, current flows from negative to positive. The electrical current contained in a circuit can be calculated by dividing the voltage by the resistance. The current is proportional to the voltage and is inversely proportional to the resistance. In this way, an increase in the voltage will result in an increase in the current. This can happen only if the resistance stays constant. If the resistance is increased and the voltage is not, the current will decrease.

Voltage (E = IR) Voltage can be described as the difference in the electrical potential between the two points in the circuit. You can calculate voltage if the currant and the resistance in the circuit are known. If either the current or the resistance results in an increase in the circuit, the voltage will automatically increase.

Resistance (R = E/I) Resistance determines how much current will pass through a component. Resistors can be used to control current and voltage levels. A high resistance will allow only a small amount of current to pass through. Conversely, a very low resistance will allow a large amount of current to pass through. Resistance is measured in ohms.

Power (P = EI) According to Ohm’s Law, power is the amount of current times the level of voltage at a given point. Power is measured in wattage or watts.

How to Measure the Ohm Value for an Inductor

Every inductor has an ohm value that changes with frequency. An inductor is a small electronic element that resists changes in an alternating current, or AC. It consists of a series of wire loops around a core that store energy in the form of a magnetic field, related to the current that passes through it. This effect, or inductance, is dependent on the material makeup and structure of the inductor. Reactance is a measure in ohms of the relationship between the inductance and frequency of the AC. Acquire the necessary data. You will need the inductance, measured in Henries, and the AC frequency, measured in Hertz. The inductance is usually written on the inductor itself or may be referenced in a schematic. The frequency is usually notated in an electronic schematic. Convert inductance as needed. Inductance is frequently expressed as micro-Henries. A henry is equal to 1,000,000 micro-henries. To convert to Henries, you would divide the number of micro-Henries by 1,000,000. Calculate reactance, in ohms, by using the formula: Reactance = 2 * π * Frequency * Inductance. π (Pi) is simply a constant, measured as 3.14.

What Is a Ferrite Clamp?

A ferrite clamp, or ferrite choke, is a device used to reduce the amount of RF (radio frequency) noise, or interference, in a wire that conducts electricity . Ferrite clamps are typically used to improve the performance of sound systems, including microphones.

Basics Ferrite is name given to ceramics formed from various metal oxides. Oxides of iron, manganese, manganese and zinc and nickel and zinc are the most common forms of ferrite.

Function Ferrite clamps usually consist of a two halves of ferrite that are, literally, clamped around a conducting wire. Ferrite is a highly permeable material and provides less resistance to the flow of magnetic flux in the conductor than air alone, so a ferrite clamps effectively absorbs some of the noise in the wire.

Limitations Ferrite may be a highly permeable, but it is also very fragile. Ferrite clamps must therefore be protected against physical damage.

How to Calculate a Solenoid

A solenoid is a coil of wire that is substantially longer than its diameter that generates a magnetic field when a current passes through it. In practice, this coil is wrapped around a metallic core and the strength of the magnetic field depends on the coil density, the current passing through the coil and the magnetic properties of the core. This makes a solenoid a type of electromagnet, the purpose of which is to generate a controlled magnetic field. This field can be used for various purposes depending on the device, from being used to generate a magnetic field as an electromagnet, to impede current changes as an inductor, or to convert the energy stored in the magnetic field to kinetic energy as an electric motor.

Magnetic Field of a Solenoid Derivation The magnetic field of a solenoid derivation can be found using Ampère's Law. We get Bl = μ₀NI where B is the magnetic flux density, l is the length of the solenoid, μ₀ is the magnetic constant or the magnetic permeability in a vacuum, N is the number of turns in the coil, and I is the current through the coil. Dividing throughout by l, we get B = μ₀(N/l)I where N/l is the turns density or the number of turns per unit length. This equation applies for solenoids without magnetic cores or in free space. The magnetic constant is 1.257 × 10⁶ H/_m. The magnetic permeability of a material is its ability to support the formation of a magnetic field. Some materials are better than others, so the permeability is the degree of magnetization a material experiences in response to a magnetic field. The relative permeability μr tells us how much this increases with respect to free space or the vacuum. μ = μ_rμ₀ where μ is the magnetic permeability and μ_r is the relativity. This tells us how much the magnetic field increases if the solenoid has a material core going through it. If we placed a magnetic material, e.g., an iron bar, and the solenoid is wrapped around it, the iron bar will concentrate the magnetic field and increase the magnetic flux density B. For a solenoid with a material core, we get the solenoid formula B = μ_r(N/l)I

Calculate Inductance of Solenoid One of the primary purposes of solenoids in electrical circuits is to impede changes in electrical current. As an electric current flows through a coil or solenoid, it creates a magnetic field that grows in strength over time. This changing magnetic field induces an electromotive force (EMF) across the coil that opposes the current flow. This phenomenon is known as electromagnetic induction. The inductance, L, is the ratio between the induced voltage v, and the rate of change in the current I. L = −v(dIdt)⁻¹ Solving for v this becomes v = −L d_I/d_t

Deriving the Inductance of a Solenoid Faraday's Law tells us the strength of the induced EMF in response to a changing magnetic field v = −nA d_B/d_t where n is the number of turns in the coil and A is the cross sectional area of the coil. Differentiating the solenoid equation with respect to time, we get Substituting this into Faraday's Law, we get the induced EMF for a long solenoid, v = −(μN²A/l)(dId_t) Substituting this into v = −L(dI/d_t) we get L = μN²A/l We see the inductance L depends on the geometry of the coil – the turns density and the cross sectional area – and the magnetic permeability of the coil material.

The Differences Between Motors & Generators

Motors and generators are electromagnetic devices. They have current -carrying loops that rotate in magnetic fields. This rapidly changing magnetic field produces electromotive forces, called emfs or voltages. Electric motors and generators are the opposite of each other. Electric motors convert electrical energy into mechanical energy, while electric generators convert mechanical energy into electrical energy.

Construction Electric motors and generators have current-carrying loops that continuously rotate in a magnetic field. The loops are wrapped around an iron core called an armature that makes the magnetic field inside of them stronger. The current in the loops reverses direction causing the armature and hence the loops to constantly rotate. The changing direction of the loops causes an induced emf to be generated. Emf is short for electromotive force. It is not a force, but is the potential difference between the terminals of a device that changes one form of energy into electrical energy. A battery, for example, converts chemical energy into electrical energy, and so is a source of emf. A potential difference is a voltage. The induced emf created by the motion of the loops becomes larger the more rapidly the magnetic field changes. This is Faraday's Law of Induction, named after its discoverer, renowned physicist Michael Faraday. AC Generators AC generators are opposite from motors, because they convert mechanical energy into that of electrical. Mechanical energy is used to rotate the loops in the magnetic field, and the generated emf is a sine wave that varies in time. Steam made from burning fossil fuels such as coal, oil and natural gas is a common source in countries like the United States. In Europe, nuclear fission is used to create steam. In some hydroelectric plants, such as those found at Niagara Falls, water pressure is used to rotate the turbines. Turbines are rotors with vanes or blades. Wind and water are not commonly used as fossil fuels for mechanical energy sources because they are not as efficient and are more costly.

AC Motors

Credit: US Department of Energy AC motors convert electrical energy into that of mechanical. An alternating current is used to rotate the loops in the magnetic field. Most AC motors produce the current by using induction. An electromagnet causes the magnetic field and uses the same voltage as the coils do.

DC Motors and Generators

Credit: US Department of Energy DC motors and generators are similar to their AC counterparts, except that they have a split ring called a commutator. The commutator is attached to electrical contacts called brushes. The changing direction of the current through the commutator causes the armature and thus the loops to rotate. The magnetic field the armature turns in may be a permanent magnet or electromagnet. DC generators have a generated emf is direct current.

Motors Compared to Generators All motors are generators. The emf in a generator increases its efficiency, but an emf in a motor contributes to energy waste and inefficiency in its performance. A back emf is a resistance to change in a magnetic field. A back emf appears in a motor after it has been turned on, though not immediately. It reduces the current in the loop, and gets larger as the speed of the motor increases.This causes the power requirements of the motor to also increase, especially under loads that are very large.

How to Calculate the Inductance of a Ferrite Inductor

Ferrity inductors are common place in electronics. Ferrite inductors have a ferrite core. Ferrite is a class of ceramic material with strong electromagnetic properties such as high permeability in combination with low electrical conductivity. Ferrite inductors are deployed in a variety of electric circuit applications such as broadband, power conversion and interference suppression.

Make a simple ferrite inductor by wrapping at least 20 turns of wire around a ferrite rod. Using an inductance meter, measure the inductance of that rod. Record the inductance as "L" and the 20 turns as "N."

Calculate the AL value of the ferrite inductor. The AL value is the base relationship between the inductance, with a given ferrite core, and the number of turns. Calculate the AL value using the following formula: AL = [(100/N)²)] x L.

For example, if your measured value of L in Step 1 is 25 uH, the corresponding AL value will be: AL = [(100/20)²] x 25uH = (5²) x 25uH = 25 x 25uh = 625 uH.

Use your AL value to calculate the inductance for various values of N using the following formula: L = AL/[(100/N)²].

For example: If N is 15, L = 625/[(100/15)²] = 625/[6.66²] = 625/44.4 = 14uH.

If N is 25, L = 625/[(100/25)²] = 625/[4²] = 625/16 = 39uH. If N is 30, L = 625/[(100/30)²] = 625/[3.33²] = 625/11.1 = 56.3uH As you can see, the inductance increases as N increases. This is because by placing more turns of wire around a loop, it concentrates the magnetic field into a smaller space, where it can be more effective and create more inductance.

How to Calculate the Winding of a Transformer

If you've ever wondered how houses and buildings use the electricity from power plants, you should learn about the transformers in power grid distributions which convert high-voltage currents to the ones you use in household appliances. These transformers use simple designs across most types of transformers, but can vary greatly in how much they change input voltage based on how they're built.

Transformer Winding Formula The transformers that power grid distributions systems use follow simple designs that use coil wound around a magnetic core in different areas. These coils of wire take incoming current and change the voltage according to the transformer turns ratio, which is: N_p/N_s = V_p/V_s for the number windings of the primary coil and secondary coil N_p and N_s, respectively, and the voltage of the primary coil and the secondary coil V_p and V_s, respectively. This transformer winding formula tells you the fraction by which a transformer changes incoming voltage and that the voltage of the winds of a coil is directly proportional to the number of windings of the coils themselves. Keep in mind that, although this formula is referred to as "ratio," it is actually a fraction, not a ratio. For example, if you had one winding in the primary coil and four windings in the secondary coil of a transformer, this would correspond to a fraction of 1/4, meaning that the transformer cuts the voltage by a value of 1/4. But the ratio 1:4 means that, for one of something, there are four of something else, which doesn't always mean the same thing as a fraction. Transformers can increase or decrease voltage, and are known as step-up or step-down transformers depending on which action they perform. This means the transformer turns ratio will always be positive, but can vary between being greater than one for step-up transformers or less than one for step-down transformers. The transformer winding formula only holds true when the angles of primary and secondary windings are in phase with one another. This means that, for a given alternating current (AC) power supply that switches back and forth between forward and reverse current, the current in both the primary and secondary windings are in sync with one another during this dynamic process. There may be some transformers with a transformer turns ratio of 1 that do not change voltage, but, instead, are used to split different circuits from one another or to slightly change the resistance of a circuit.

Transformer Design Calculator You can understand the properties of transformers to determine what a transformer design calculator would take into account as a method of determining how to construct transformers themselves. Though the primary and secondary windings on a transformer are separate from one another, the primary winding induces a current in the secondary windings through a method of inductance. When an AC power supply is sent through the primary windings, current flows through the turns and creates a magnetic field through a method called mutual inductance.

Transformer Winding Formula and Magnetism Magnetic field describes in what direction and how strong magnetism would act on a moving charged particle. The maximum value of this field is: dΦ/dt , the rate of change of magnetic flux Φ over a small period of time. Flux is a measurement of how much magnetic field flows through a specific surface area such as a rectangular area. In a transformer, the magnetic field lines are sent outward from the magnetic coil around which the wires are wound. The magnetic flux links both of the windings together, and the magnetic field's strength depends on the amount of current and the number of windings. This can give us a transformer design calculator that takes into account these properties. Faraday's law of inductance that describes how magnetic fields are induced in materials dictates that the voltage by either windings induced for either primary windings or secondary windings. This is usually referred to as the induced electromotive force (emf). If you were to measure the change in magnetic flux over a small period of time, you could obtain a value of: dΦ/d_t and use it to calculate the emf. The general formula for magnetic flux is: Φ = BA∣cosθ for magnetic field B, surface area of the plane in the field A and the angle between the magnetic field lines and the direction perpendicular to the area θ. You can account for the geometry of the windings around the magnetic core of the transformer to measure flux askat for an AC power supply where ω is the angular frequency (2πf for frequency f) and Φmax is the maximum flux. In this case, frequency f refers to the number of waves that pass a given location each second. Engineers also refer to the product of current times the number of turns of windings as "ampere-turns," a measure of the coil's magnetizing force.

Transformer Winding Calculator Examples If you wanted to compare the experimental results of how the windings of transformers affect their use, you can compare the observed experimental properties to those of a transformer winding calculator. The software company Micro Digital offers an online Transformer Winding Calculator for calculating Standard Wire Gauge (SWG) or American Wire Gauge (AWG). This lets engineers manufacture wires with the appropriate thickness so they can carry wire charges necessary for their purposes. The transformer calculator turns tells you the individual voltage through each turn of the winding. Other calculators like the one from the manufacturing company Flex-Core let you calculate the wire size for different practical applications if you enter in the burden rating, the nominal secondary current, the wire length between the current transformer and meter and the input burden of the meter. The current transformer creates an AC voltage supply in its secondary winding that's proportional to the current in the primary winding. These transformers reduce high voltage currents to lower values using an easy method of monitoring the actual electrical current. The burden is the resistance of the measuring instrument itself to the current sent through it. Hyperphysics offers an online Transformer Power Calculation interface that lets you use as transformer design calculator or as a transformer resistance calculator. To use it, you need to input a supply voltage frequency, a primary winding inductance, secondary winding inductance, primary winding number of coils, secondary winding number of coils, secondary voltage, primary winding resistance, secondary winding resistance, secondary winding load resistance and mutual inductance. The mutual inductance M accounts for the effect that change in load on secondary coil can exert on the current through the primary with an emf: emf = −M ΔI₁/Δ_t for change in current through the primary coil ΔI1 and change in time Δt. Any online transformer winding calculator makes assumptions about the transformer itself. Make sure you know how each website calculates the values i claims to do so that you can understand the theory and principles behind transformers in general. How close they are to the transformer winding formula that follows from the physics of a transformer depends on these properties.

Calculate the Winding of a Transformer How to Calculate the Winding of a Transformer The alternating current (AC) in most of the appliances in your home can only come from power lines that send direct current (DC) through use of a transformer. Through all the different types of current that may flow through a circuit, it helps to have the power to control these electrical phenomena. For all their uses in changing the voltage of circuits, transformers rely heavily on their turns ratio.

Calculating Transformer Turns Ratio A transformer turns ratio is the division of the number of turns in the primary winding by the number of turns in the secondary winding by the equation T_r = N_p/N_s This ratio should also equal the voltage of the primary winding divided by the voltage of the secondary winding, as given by V_p/V_s. The primary winding refers to the powered inductor, a circuit element that induces a magnetic field in response to the flow of charge, of the transformer, and the secondary one is the unpowered inductor. These ratios hold true under the assumption that the phase angle of the primary winding equals the phase angles of the secondary by the equation ΦP = ΦS. This primary and secondary phase angle describes how the current, which alternates between forward and reverse directions in the primary and secondary windings of the transformer, are in-sync with one another. For AC voltage sources, as used with transformers, the incoming waveform is sinusoidal, the shape a sine wave produces. The transformer turns ratio tells you how much the voltage changes through the transformer as current passes from the primary windings to the secondary windings. Also, please note that the word "ratio" in these formula refer to a fraction, not an actual ratio. The fraction of 1/4 is different from the ratio 1:4. While 1/4 is one part out of a whole that is divided into four equal parts, the ratio 1:4 represents that, for one of something, there are four of something else. The "ratio" in the transformer turns ratio is a fraction, not a ratio, in the transformer ratio formula. The transformer turns ratio reveals that the fractional difference that the voltage takes based on the number of coils wound around the primary and secondary parts of the transformer. A transformer with five primary wound coils and 10 secondary wound coils will cut a voltage source in half as given by 5/10 or 1/2. Whether voltage increases or decreases as a result of these coils determines of it's a step-up transformer or step-down transformer by the transformer ratio formula. A transformer that neither increases nor decreases voltage is an "impedance transformer" that can either measure impedance, a circuit's opposition to current, or simply indicate breaks between different electrical circuits.

The Construction of a Transformer The core components of a transformer are the two coils, primary and secondary, that wrap around an iron core. The ferromagnetic core, or a core made from a permanent magnet, of a transformer also uses thin electrically insulated slices so that these surfaces can decrease resistance for the current that passes from the primary coils to the secondary coils of the transformer. The construction of a transformer will generally be designed to lose as little energy as possible. Because not all of the magnetic flux from the primary coils pass to the secondary, there will be some loss in practice. Transformers will also lose energy due to eddy currents, localized electric current caused by changes in the magnetic field in electrical circuits. Transformers get their name because they use this setup of a magnetizing core with windings on two separate parts of it to transform electrical energy into magnetic energy through the magnetizing of the core from the current through the primary windings. Then, the magnetic core induces a current in the secondary windings, which converts the magnetic energy back into electrical energy. This means that transformers always operate on an incoming AC voltage source, one that switches between forward and reverse directions of current at regular intervals.

Types of Transformer Effects Aside from the voltage or number of coils formula, you can study transformers to learn more about the nature of different types of voltages, electromagnetic induction, magnetic fields, magnetic flux and other properties that result from the construction of a transformer. In contrast to a voltage source that sends current in one direction, an AC voltage source sent through the primary coil will create its own magnetic field. This phenomena is known as mutual inductance. The magnetic field strength would increase to its maximum value, which is equal to the difference in magnetic flux divided by a period of time, dΦ/dt. Keep in mind, in this case, Φ is used to indicate magnetic flux, not phase angle. These magnetic field lines are drawn outward from the electromagnet. Engineers building transformers also take into account the flux linkage, which is the product of the magnetic flux Φ and the number of coils in the wire N caused by the magnetic field passing from one coil to the other. The general equation for magnetic flux is Φ = BA cosθ for a surface area which the field goes through A in m2, magnetic field B in Teslas and θ as the angle between a perpendicular vector to the area and the magnetic field. For the simple case of wrapped coils around a magnet, the flux is given by Φ = NBA for number of coils N, magnetic field B and over a certain area A of a surface that is parallel the magnet. However, for a transformer, the flux linkage causes the magnetic flux in the primary winding to equal that of the secondary winding. According to Faraday's Law, you can calculate the voltage induced in the primary or secondary windings of the transformer by calculating N x dΦ/dt. This also explains why the transformer turns ratio of the voltage of one part of the transformer to the other is equal to the number of coils of one to the other. If you were to compare the N x dΦ/dt of one part to the other, the dΦ/dt would cancel out due to both parts having the same magnetic flux. Finally, you can calculate a transformer's ampere-turns as the product of current times the number of coils as a method of measuring the magnetizing force of the coil

Transformers in Practice Power distributions grids send electricity from power plants to buildings and houses. These power lines begin at the power plant where an electrical generator creates electrical energy from some source. This could be a hydroelectric dam that harnesses the power of water or a gas turbine that uses combustion to create mechanical energy from natural gas and converts it to electricity. This electricity is, unfortunately, produced as DC voltage which needs to be converted to AC voltage for most home appliances. Transformers make this electricity usable by creating single-phase DC power supplies for households and buildings from the incoming oscillating AC voltage. The transformers along power distribution grids also ensure the voltage is an appropriate amount for house electronics and electricity systems. Distributions grids also uses "buses" that separate distribution into multiple directions alongside circuit breakers to keep separate distributions distinct from one another. Engineers often account for the efficiency of transformers using the simple equation for efficiency as: η = P_o / P_i for output power P_o and input power P_i. Based on the construction of transformer designs, these systems don't lose energy to friction or air resistance because transformers don't involve moving parts. The magnetizing current, the amount of current necessary to magnetize the core the transformer, is generally very small compared to the current that the primary part of a transformer induces. These factors mean that transformers are typically very efficient with efficiencies of 95 percent and up for most modern designs. If you were to apply an AC voltage source to the primary winding of a transformer, the magnetic flux that's induced in the magnetic core will continue to induce an AC voltage in the secondary winding in the same phase as the source voltage. The magnetic flux in the core, however, remains 90° behind the phase angle of the source voltage. This means the primary winding's current, the magnetizing current, also lags behind the AC voltage source.

Transformer Equation in Mutual Inductance In addition to field, flux and voltage, transformers illustrate the electromagnetic phenomena of mutual inductance that gives more power to the primary windings of a transformer when hooked to an electrical supply. This happens as the primary winding's reaction to an increase in load, something that consumes power, on the secondary windings. If you added a load to the secondary windings through a method such as increasing the resistance of its wires, the primary windings would respond by drawing more current from the power source to compensate for this decrease. Mutual inductance is the load you put on the secondary you can use to calculate the increase in current through the primary windings. If you were to write a separate voltage equation for both the primary and secondary windings, you could describe this phenomena of mutual inductance. For the primary winding, Vp = I_pR₁ + L₁ ΔI_p/Δ_t - M ΔI_s/Δ_t for current through the primary winding I_p, primary winding load resistance R₁, mutual inductance M, primary winding inductance L₁, secondary winding I_s and change in time Δ_t. The negative sign in front of the mutual inductance M shows that source current immediately experiences a drop in voltage due to the load on the secondary winding, but, in response, the primary winding raises its voltage. This equation follows the rules of writing equations that describe how current and voltage differ among circuit elements. For a closed electrical loop, you may write the sum of the voltage across each component as equal to zero to show how voltage drops across each element in the circuit. For the primary windings, you write this equation to account for the voltage across the primary windings themselves (I_pR₁) , the voltage due to the induced current of the magnetic field L₁ΔI_p/Δ_t and the voltage due to the effect of mutual inductance from the secondary windings M ΔI_s/Δ_t. Similarly, you may write an equation that describes the voltage drops across the secondary windings as M ΔI_p/Δ_t = I_sR₂ + L₂ ΔI_s/Δ_t This equation includes the secondary winding current Is, secondary winding inductance L₂ and the secondary winding load resistance R2. The resistance and inductance are labeled with a subscripts 1 or 2 instead of P or S, respectively, as resistors and inductors are often numbered, not denoted using letters. Finally, you can calculate mutual inductance from the inductors directly as M = L₁L₂

How to Size a Transformer KVA

Transformers are sized to support the electrical load. A transformer is an electrical device used to convert power from the source, usually a utility company, to the power required by the load. The load can be a house, building or any other electrical system or appliance. The transformer consists of a primary and secondary winding where, when input power is supplied to the primary winding, the transformer converts it and sends the power on to the load via the outputs leads of the secondary winding. Transformers are rated or sized in terms of KVA, the power level in kilovolt-amperes. Find the input voltage required by the electrical load connected to transformer secondary winding. Call this value "Vload." Refer to the electrical schematic of the load. As an example, assume Vload is 120 volts. Find the current flow required by the electrical load. Call this value "Iload." Refer to the electrical schematic of the load. If the value of Iload is not available, find the input resistance, or "Rload," and calculate Iload by dividing Vload by Rload. As an example, assume Iload is 30 amperes. Determine power requirements of the load in kilowatts, or "KW." Call it KWload. Use the formula: KWload = (Vload x Iload)/1000. Continuing with the example numbers: KW = (120 x 30)/1000 = 3600/1000 = 3.6 KW Find the power in kilovolts-amperes, or KVA, required to deliver the KW in Step 3 to the load using the formula: KVA = KW/0.8 (0.8 is the typical power factor associated with a load). Continuing with the example’s numbers: KVA = 3.6/0.8 = 4.5 KVA. Locate and install a transformer rated at the KVA level found in Step 4 or slightly higher. For example, transformers are purchased in standard KVA sizes such as 5 KVA, 10 KVA, 15 KVA and so on. In the example in which KVA is 4.5, a 5 KVA transformer will apply.

How to Calculate Transformer VA Rating

Difference Between an Electrical Inverter & Transformer Transformers are the backbone of power distribution systems. The VA rating refers to the power distribution rating relative to how much power the transformer can deliver to the load. To calculate VA, you need to know the supply voltage and the current delivered to the load. You get the supply voltage from the voltage specifications associated with the primary and secondary windings. You then apply the voltage and measure the current that appears across the load. Find the primary and secondary voltage of the transformer by referring to the transformer specifications. As an example, assume that the primary is 480 volts and the secondary is 208 volts. Turn off power to the system. Put on electrical safety gloves and follow standard electrical safety precautions. Connect the secondary side of the transformer to the electrical load. Connect an ammeter in parallel between the secondary side of the transformer and the load. Connect a power supply to the primary side of the transformer. Ensure that the power supply is capable of delivering the primary voltage to the transformer. Using the example numbers, you will ensure that the power supply can deliver 480 volts, which is the primary voltage. Power up the power supply to the primary voltage level of the transformer. Note and record the amperes registered on the ammeter. Call this value "I," and assume, as an example, that it equals 65 amps. Calculate the VA rating using the formula "VArating = (Vsecondary x I)/0.8," where Vsecondary is the secondary voltage of the transformer and the 0.8 accounts for the power factor of the load. Continuing with the example: VArating = (208 x 65)/0.8 = 16,900 volt-amperes, or 16.9 kilovolt-amperes, or 16.9 KVA.