Question

Time constant of the given circuit is $\tau$ . If the battery is replaced by an ac source having voltage $V=V_{0}cos \omega t$ , power factor of the circuit will be

• A. $\omega \tau$
• B. $\frac{1}{\sqrt{1 + \left(\omega \tau\right)^{2}}}$
• C. $\sqrt{1 - \left(\omega \tau\right)^{2}}$
• D. None

Answer 1

Answer: (B)

For DC LR circuit, time constant is given by,
$\tau=L/R$
For AC LR circuit, power factor is given by,

$cos \phi = \frac{R}{\sqrt{R^{2} + \omega ^{2} L^{2}}}=\frac{1}{\sqrt{1 + \omega ^{2} \frac{L^{2}}{R^{2}}}}=\frac{1}{\sqrt{1 + \omega ^{2} \tau^{2}}}$