Question

. (i) Explain the term ‘inductive reactance’. Show

graphically the variation of inductive reactance

with frequency of the applied alternating

voltage.

(ii) An ac voltage E = E0 sin wt is applied

across a pure inductor of inductance L. Show

mathematically that the current owing through

it lags behind the applied voltage by a phase

angle of p/2.

Answer 1

Inductive Reactance:

• It is the resistance provided by an inductor in an AC circuit against the flow of current.

Graph:

• The graph has been attached.

Mathematical proof:

$E = E_{0} \sin( \omega t)$

$\implies \:L \: \dfrac{di}{dt} = E_{0} \sin( \omega t)$

$\implies \: \: \dfrac{di}{dt} = \dfrac{E_{0}}{L} \sin( \omega t)$

$\displaystyle\implies \: \int di = \dfrac{E_{0}}{L} \int \sin( \omega t) \: dt$

$\displaystyle\implies \: i= \dfrac{E_{0}}{\omega L} \bigg \{ - \cos( \omega t) \bigg \}$

$\displaystyle\implies \: i= \dfrac{E_{0}}{\omega L} \bigg \{ - \sin( \dfrac{\pi}{2} - \omega t) \bigg \}$

$\displaystyle\implies \: i= \dfrac{E_{0}}{\omega L} \bigg \{ \sin( \omega t - \dfrac{\pi}{2} ) \bigg \}$

So, current lags behind voltage by π/2.