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,

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