Alternating Current Ques 19
19. Power dissipated in an $LCR$ series circuit connected to an $a.c$ source of emf $\varepsilon$ is
[2009]
(a) $\frac{\varepsilon^{2} \sqrt{R^{2}+(L \omega-\frac{1}{C \omega})^{2}}}{R}$
(b) $\frac{\varepsilon^{2}[R^{2}+(L \omega-\frac{1}{C \omega})^{2}]}{R}$
(c) $\frac{\varepsilon^{2} R}{\sqrt{R^{2}+(L \omega-\frac{1}{C \omega})}^{2}}$
(d) $\frac{\varepsilon^{2} R}{[R^{2}+(L \omega-\frac{1}{C \omega})^{2}]}$
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Answer:
Correct Answer: 19.(d)
Solution:
- (d) Power dissipated in series $LCR$;
$P=I^{2} R=\frac{\varepsilon^{2}}{(Z)^{2}} R$
$=\frac{\varepsilon^{2} R}{[R^{2}+(\omega L-\frac{1}{\omega C})^{2}]}$ $Z=\sqrt{R^{2}+(\omega L-\frac{1}{\omega C})^{2}}$
is called the impedance of the circuit.
BETA
