Inductance

As the current in a coil of wire increases or decreases -- aka, changes -- the flux through the coil changes as well. This changing flux induces a back emf in the same coil. Since the change in flux is proportional to the change in the current, and opposes that change, we can write the relationship

where L, the inductance, represents a proportionality constant that reflects the coil's geometry. Inductance is measured in a unit called a Henry (H) which is a V sec/amp or J sec²/C².

The most common inductor is a solenoid. Let's derive an expression for its inductance. An induced emf can be written as

Setting these two expressions equal to each other, yields

As the current changes from zero to I, the flux changes from zero to f, therefore Df = f and Di = I and our expression becomes

Notice that this expression, as predicted, deals only with the geometry of the solenoid: its cross-sectional area, length, and total number of coils.

When an inductor is part of a circuit, the current does not instantaneously reach its maximum value of I = e/R, instead the current builds gradually depending on the ratio of L/R.