Question

In an AC circuit, a resistance of R ohm is connected in series with an inductor of self inductance L. If phase angle between voltage and current be $45^{\circ}$, the value of inductive reactance $(X_L)$ will be equal to

• A. R
• B. $ \frac{ R}{ 8} $
• C. $ \frac{ R}{ 4} $
• D. $ \frac{ R}{ 2} $

Answer 1

Answer: (A)

The phasor diagram in L-R circuit is given below.

Given, the phase angle between voltage and current
$ \phi = 45^\circ$
So, $ \tan \, \phi = \frac{ V_L}{ V_R} = \frac{ IX_L}{ IR} $
Here, $ X_L$ = inductive reactance
$\Rightarrow \tan \, 45^{\circ} = \frac{ X_L}{ R} $
$\Rightarrow 1 = \frac{ X_L}{ R} \Rightarrow X_L = R $