Question

A 20 kω resistor is connected in series with an initially uncharged 100 μf capacitor and a 5 v battery. What is the charge on the capacitor when the circuit has reached steady state?

Answer 1

Hi there!

We can use the equation for the charge of a charging capacitor:
$q(t) = C\epsilon( 1 - e^{-\frac{t}{RC}})$

Using Capacitor equations:
$C = \frac{Q}{V}}\\\\Q = CV$

Therefore, Cε equals the steady-state charge of the capacitor (the function approaches this value as t ⇒ ∞.

We can plug in the givens and solve.
$\epsilon = 5 V\\\\C = 100\mu F = 0.0001 F$

$Q = C \epsilon = (0.0001)(5) = \boxed{0.0005 C}$