Alternating Current - Result Question 24
24. 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) $\varepsilon^{2}[R^{2}+(L \omega-\frac{1}{C \omega})^{2}]$
(c) $\sqrt{R^{2}+(L \omega-\frac{1}{C \omega})^{2}}$
(d)
$ \frac{\varepsilon^{2} R}{[R^{2}+(L \omega-\frac{1}{C \omega})^{2}]} $
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Answer:
Correct Answer: 24. (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.
