## Inductors

An inductor can be made physically using a coil of wire, and it stores magnetic flux when a current flows through it. Figure E.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

 (E.3)

where denotes the inductor's stored magnetic flux at time , is the inductance in Henrys (H), and is the current through the inductor coil in Amperes (A), where an Ampere is a Coulomb (of electric charge) per second. Differentiating with respect to time gives

 (E.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.

#### Mechanical Equivalent of an Inductor is a Mass

The mechanical analog of an inductor is a mass. The voltage across an inductor corresponds to the force used to accelerate a mass . The current through in the inductor corresponds to the velocity of the mass. Thus, Eq.(E.4) corresponds to Newton's second law for an ideal mass:

where denotes the acceleration of the mass .

From the defining equation for an inductor [Eq.(E.3)], we see that the stored magnetic flux in an inductor is analogous to mass times velocity, or momentum. In other words, magnetic flux may be regarded as electric-charge momentum.

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