Question

The time constant of a capacitor is 5sec. If the capacitance is C=100nF and it is charged from zero by a cell of EMF 10V through a resistor. What is the charge on it after 3 seconds?

• A. $4\times {10}^{-7}C$
• B. $4.5\times {10}^{-7}C$
• C. $5\times {10}^{-7}C$
• D. $5.5\times {10}^{-7}C$

Answer 1

The correct option is B $4.5\times {10}^{-7}C$

Use the equation,
$q=CE(1-e^{-\frac{t}{RC}})$
We know that time constant, $\tau =RC=5s$
So,
At t=3,
$q=100\times {10}^{-9}\times 10(1-e^{-\frac{3}{5}})$
$q={10}^{-6}\left(0.451\right)$
$q=4.51\times {10}^{-7}C$