Example from Physics, 19.1 Ohm's law

Average Current to Charge a Capacitor

In a circuit containing a capacitor and a resistor, it takes 1 min to charge a 16 μF capacitor by using a 9-V battery. What is the average current during this time?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
We can determine the charge on the capacitor by using the definition of capacitance: $C = \frac{Q}{V}$ . When the capacitor is charged by a 9-V battery, the voltage across the capacitor will be $V = 9 V$ . This gives a charge of

$\begin{matrix} C & = & \frac{Q}{V} \\ Q & = & C V . \end{matrix}$
19.4

By inserting this expression for charge into the equation for current, $I = \frac{Δ Q}{Δ t}$ , we can find the average current.
Solution
The average current is

$\begin{matrix} I & = & \frac{Δ Q}{Δ t} \\ = & \frac{C V}{Δ t} \\ = & \frac{(16 \times 10^{−6} F) (9 V)}{60 s} \\ = & 2.4 \times 10^{−6} A \\ = & 2.4 μA. \end{matrix}$
19.5

0 of 2 steps open

How did it go?

Strategy

Solution