First slide

Capacitance

Question

A $16 μ F$ capacitor, initially charged to 5V, is started charging at t=0 by a source at the rate of $40 t μ C / s$ . How long will it take to raise its potential to 10V?

Difficult

A

2 s
B

1 s
C

3 s
D

0.2 s

Solution

$q = C V \frac{d q}{d t} = C \frac{d V}{d t} 40 t x 10^{- 6} = C \frac{d V}{d t} 40 t x 10^{- 6} d t = 16 x 10^{- 6} d V o n i n t e g r a t i n g 40 \frac{t^{2}}{2} = 16 (10 - 5) = 80 t = 2 s$

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