A device that can induce a voltage when current is changed is said to have inductance. A typical inductor is a coil of wire in the form of a solenoid. Inductance is measured in henrys which is denoted by H.
A current flowing through a conductor induces a magnetic field. In the case of a wire, coiling the wire into the form of a solenoid increases the strength of the field and we can calculate the magnetic field strength B (measured in teslas) as follows:
B = μ0IN/l
where I is current, N is the number of turns of the wire, l is the length of the wire, and μ0 is the permeability of free space (4×π×10-7 Hm-1 = 1.2566×10-6 Hm-1).
A change in current leads to a change in magnetic field and an EMF is induced in the coil which opposes the change in current. We can calculate the voltage with the following:
V = -dΦ/dt = -μ0AN/l di/dt
where Φ is magnetic flux and this is calculated by Φ=B×A where B is magnetic field strength, and A is the cross-sectional area of the coil.
This is the voltage induced in each turn of the wire. To calculate the total voltage induced in the coil we just multiply by N to give
Vcoil = -μ0AN2/l di/dt
Inductance (L) in henrys is given by
L = -μ0AN2/l
So the voltage across an inductor can be more simply written as:
Vcoil = L di/dt
Fischer-Cripps. A.C., The Electronics Companion. Institute of Physics, 2005.
Copyright © 2014 Barry Watson. All rights reserved.