Question

An uncharged 10 mF capacitor is connected to a 12-volt battery. When it is disconnected
2 msec later the voltage across the capacitor is 2 volts. Calculate the internal resistance of the battery.

Answer 1

Capacitance of the capacitor is

Potential difference across the battery is

Time elapsed

Voltage across capacitor at time t is

Let R be the internal resistance of the battery. The capacitance and the battery (including its internal resistance) forms a RC circuit. The voltage across the capacitor during charging is

We want to solve for R

Taking natural logarithm on both sides,

Using ln(e^x)=x we get

Substituting values