Inductive Reactance

When an alternating current of constant amplitude is passed through the winding of an air-core inductance, energy is alternately stored and given up every quarter cycle. If the resistance of the circuit is negligible, all of the energy that is stored in the magnetic field during one quarter cycle is reversible and is returned to the source during the following quarter cycle. The average power consumed by such a circuit is zero during a number of complete cycles.

Let L = self-inductance in henrys

i = I sin ωt
where I = rms or effective value of the current

ω = 2πf
where f = frequency in cycles per second

If the resistance is negligible, the applied voltage is

[4-99]

In Eq. 4-99, V is the rms value of the voltage applied to the self-inductance. Also

[4-100]

where X is the inductive reactance.

From Eqs. 4-98 and 4-99, it is evident that the current lags the voltage by 90°. The relationship between the voltage and current for a circuit of constant self-inductance and negligible resistance is shown in Fig. 4-8(a) and 4-8(c). The instantaneous power is shown graphically as a function of time in Fig. 4-8(b).

Figure 4-8. (a) Voltage and current waves, (b) power wave, (c) phasor diagram for pure self-inductance