Question

A 500 uF capacitor is charged at a steady rate of 100 uC/s.
The potential difference across the capacitor will be 10 V
after an interval of
(a) 5 s
(b) 25 s
(C) 20 s
(d) 50 s​

Answer 1

Explanation

Answer:

$50s$

Answer 2

After 50 sec potential difference across capacitor will be 10 volt

So option (d) will be correct answer

Explanation:

We have given capacitance of the capacitor is $C=500\mu F$

Rate of change of charge $\frac{dQ}{dt}=100\mu C/sec$

We know that charge $Q=CV$

Now differentiating both side

$\frac{dQ}{dt}=C\frac{dV}{dt}$

$100=500\times \frac{dV}{dt}$

$\frac{dV}{dt}=\frac{1}{5}$

$dV=\frac{1}{5}dt$

Now integrating both side

$[V]_0^{10}=\frac{1}{5}\times [t]_0^t$

$\frac{t}{5}=10$

t = 50 sec

So option (D) will be correct answer

Learn more

A capacitor of 20 uF and charged to 500 V:

connected in parallel to another capacitor of

charged to 200 V. The common potential

(a) 200 V (b) 400 V (C) 800 V (d) 160​

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