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. $\bigg( \frac{ R^2 + \omega^2 \, L^2 }{ V} \bigg)$
• B. $\frac{ V^2 \, R }{ (R^2 + \omega^2 \, L^2 )}$
• C. $\bigg( \frac{ V}{ R^2 + \omega^2 \, L^2 } \bigg)$
• 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 = $V i \cos \, \phi$ + V $\bigg( \frac{ V}{ Z} \bigg) \bigg( \frac{ R}{ Z} \bigg)$ = $\frac{ V^2 \, R}{ Z^2 }$ = $\frac{ V^2 \, R}{ ( R^2 + \omega^2 \, L^2 ) }$