The ability of an electrical conductor, such as coil, to produce induced voltage when the current flowing through it varies is called inductance. To calculate the inductance of a coil based on its physical construction, you can use this equation where:
L - Inductance of coil in Henrys (H)
N - Number of turns
μr - Permeability of the core
μo - Permeability of air or vacuum (1.26X10–6)
A - Area enclosed
l - Coil length
Coils of wire manufactured to have a definite value of inductance are called inductors.
Inductor Voltage-Current Relationship
This equation shows the voltage-current relationship in an inductor where:
v is the induced voltage
L is the inductance of the inductor
di/dt is the instantaneous rate of change of the current through the inductor
The induced voltage across an inductor is directly proportional to its inductance and the instantaneous rate of change of the current through the inductor. So the greater the rate of change of current through the coil, the higher is the induced voltage. However, if the current through the inductor doesn’t change at a particular instant, the induced voltage is zero.
Inductive reactance (XL) is the measure of inductor’s opposition to the flow of sine-wave alternating current. It depends on the amount of inductance and the frequency of the voltage applied. To determine the reactance of an inductor, you can use this equation.
Inductor Energy Stored
Just like a capacitor, ideally, an inductor does not dissipate the electrical energy supplied to it by the voltage source. The energy, however, is stored in a magnetic field. To calculate the energy stored in an inductor, you can use this equation.
k - Coefficient of coupling
Two coils have mutual inductance when the current in one coil can induce a voltage in the other coil. As you can see in the diagram, if L1 is connected to a voltage source, though not physically, L1 and L2 are linked by a magnetic field. A changing current in L1 can induce voltage both across L1 and L2. If a load is connected across L2, the induced voltage across L2 can supply a current to that load. You can use this equation to calculate the mutual inductance between the two coils.
Total Inductance of Two Series Coils with Mutual Inductance
The total inductance of two series coils with mutual inductance (LT) depends on the amount of mutual coupling and on whether if they are connected series-aiding or series-opposing. The coils are connected series-aiding when the common current produces the same direction of magnetic field for the two coils. They are connected series-opposing when their magnetic field has opposite direction.
The mutual inductance (LM) is plus and increases more the total inductance when the two coils are series-aiding. In series-opposing, the mutual inductance is minus and reduces the total inductance of the two series coils.
Series Inductors Equivalent Inductance
Parallel Inductors Equivalent Inductance
When inductors are connected in parallel, the total or equivalent inductance (Leq) is calculated the same way with parallel resistors. The equivalent inductance (Leq) can be determined by inverting the sum of the inverses of all inductances. Again, in this calculation, it is assumed that there’s no mutual induction between the inductors.