Alternating Current Ques 3
3. A $40 $ $ \mu F$ capacitor is connected to a $200 $ $V, 50 $ $Hz$ ac supply. The rms value of the current in the circuit is, nearly:
[2020]
(a) $2.05 $ $A$
(b) $2.5 $ $A$
(c) $25.1 $ $A$
(d) $1.7 $ $A$
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Answer:
Correct Answer: 3.(b)
Solution:
- (b) Given :
Capacitance, $C=40 $ $\mu F=40 \times 10^{-6} $ $F$
Frequency, $f=50$ $ Hz$
$\therefore \omega=2 \pi f=100 \pi$
$\varepsilon _{\text{rms }}=200$ $ V$
$\therefore I _{\text{rms }}=\frac{\varepsilon _{\text{rms }}}{X_C}=\frac{\varepsilon _{\text{rms }}}{\frac{1}{C \omega}}$
$ =200 \times 40 \times 10^{-6} \times 2 \pi \times 50=2.5 $ $A \text{. } $
BETA
