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Inductors

An inductor can be made physically using a coil of wire, and it stores magnetic flux when a current flows through it. Figure C.2 shows a circuit in which a resistor is in series with the parallel combination of a capacitor and inductor .

The defining equation of an inductor is

 (C.3)

where denotes the inductor's stored magnetic flux at time , is the inductance in Henrys, and is the current through the inductor coil in Coulombs. Differentiating with respect to time gives

 (C.4)

where is the voltage across the inductor in volts. Again, the current is taken to be positive when flowing from plus to minus through the inductor.

Taking the Laplace transform of both sides gives

by the differentiation theorem for Laplace transforms.

Assuming a zero initial current in the inductor at time 0, we have

Thus, the driving-point impedance of the inductor is . Like the capacitor, it can be analyzed in steady state (initial conditions neglected) as a simple resistor with value Ohms.

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