First slide

Capacitors and capacitance

Question

A $16 μF$ capacitor, initially charged to 5 V, is started charging at t = 0 by a source at the rate of $40 t {μCs}^{- 1}$ . How long will it take to raise its potential to 10V?

Moderate

A

1 s
B

2 s
C

3 s
D

none of these

Solution

$q_{i} = {CV}_{i} = 16 \times 5 = 80 μC, q_{f} = {CV}_{f} = 16 \times 10 = 160 μC$
Given $\frac{dq}{dt} = 40 t \Rightarrow \int_{q_{i}}^{q_{f}} dq = \int_{0}^{t} 40 t$
or $q_{f} - q_{i} = \frac{40 t^{2}}{2}$
or $160 - 80 = 20 t^{2} or t = 2 s$

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