Question

An inductor of inductance L and resistor of resistance R are joined in series and connected by a source of frequency $\omega$. Power dissipated in the circuit is

• A. $\frac{(R^{2} + \omega^{2}L^{2})}{V}$
• B. $\frac{V^{2}R}{(R^{2} + \omega^{2}L^{2})}$
• C. $\frac{V}{(R^{2} + \omega^{2}L^{2})}$
• D. $\frac{\sqrt{R^{2} + \omega^{2}L^{2}}}{V^{2}}$

Answer 1

Answer: (B)

$\frac{V^{2}R}{(R^{2} + \omega^{2}L^{2})}$

Answer 2

$P = Vi\cos\varphi = V\mspace{6mu}\left( \frac{V}{Z} \right)\mspace{6mu}\left( \frac{R}{Z} \right) = \frac{V^{2}R}{Z^{2}} = \frac{V^{2}R}{(R^{2} + \omega^{2}L^{2})}$