Alternating Current Ques 7
7. An inductor $20$ $ mH$, a capacitor $100$ $ \mu F$ and a resistor $50 $ $\Omega$ are connected in series across a source of emf, $V=10 \sin 314 $ $t$. The power loss in the circuit is
[2018]
(a) $0.79 $ $W$
(b) $0.43 $ $W$
(c) $1.13 $ $W$
(d) $2.74$ $ W$
Show Answer
Answer:
Correct Answer: 7.(a)
Solution:
- (a) Power dissipated in an LCR series circuit connected to an a.c. source of emf E
$P=E _{\text{rms }} i _{rms} \cos \phi=\frac{E _{r m s}^{2} R}{Z^{2}}=\frac{E _{r m s}^{2} R}{R^{2}+(\omega L-\frac{1}{C \omega})^{2}}$
$=\frac{(\frac{10}{\sqrt{2}})^{2} \times 50}{(50)^{2}+(314 \times 20 \times 10^{-3}-\frac{1}{314 \times 100 \times 10^{-6}})^{2}}$
Solving we get, $P=0.79 $ $W$
BETA
