Question

If a capacitor of $10\mu F$ is charged to 10V and then connected to a new circuit to discharge through a $10\Omega$ resistor, what is the charge on it after $20\mu s$?

• A. $72\mu C$
• B. $92\mu C$
• C. $82\mu C$
• D. $62\mu C$

Answer 1

The correct option is C $82\mu C$

You have to know the capacitor discharge equation -
$q=Q{e}^{-\frac{t}{RC}}$
Ok, this is what we need to use. But, do we know everything we need for the equation?
We know, $C=10\mu F$
$R=10\Omega$
$t=20\mu s$
But what is Q?
Q is the initial charge on the capacitor. How do we find it?
We're given that the capacitor is charged to 10V. So use the equation Q=CV
$Q=10\times {10}^{-6}\times 10$
$Q=100\mu C$
Now use our equation.
$q=Q{e}^{-\frac{t}{RC}}$
$q=100\times {10}^{-6}{e}^{-\frac{20}{10\times 10}}$
$q=82\mu C$