A.C. Through Pure Inductance alone

A.C. THROUGH PURE INDUCTANCE ALONE

Fig. 1.60(a) shows the circuit containing a pure inductance of L henry.

Consider the alternating voltage applied across the circuit be given by the equation,

Whenever an alternating voltage is applied to a purely inductive coil, a back e.m.f. is induced due to the self-inductance of the coil. This back e.m.f. opposes the rise or fall of the current through the coil. Since there is no ohmic drop in this case, hence the applied voltage has to overcome this induced e.m.f. only.

where XL = ωL (opposition offered to the flow of alternating current by a pure XL inductances) and is called Inductive reactance. It is given in ohms if L is in henry and o is in radian / second.

The value of current will be maximum when sin

Substituting this value in equation (2), we get

Power

Hence average power consumed in a pure inductive circuit is zero.

Hence in a pure inductive circuit, we have :

1. Current

2. Current always lags behind the voltage by 90°.

3. Average power consumed is zero.

Variation of XL and ƒ:

Since XL = ωL = 2πfL, and here if L is constant, then

XL ∝ f

Fig. 1.61, shows the variation. As frequency is increased XL increases and the current taken by the circuit decreases.