Answer to Question #115811 in Electricity and Magnetism for Ishmael

Question

A 2f capacitor is charged to a potential difference of 200v, then the supply is disconnected. The capacitor is then connected to another uncharged capacitor. The potential difference across the parallel arrangement is 80v. Find the capacitance of the second capacitor.

Answer 1

The 2F capacitor connected to 200 V acquires a charge of

$$Q=V_1C_1.$$

We know that charges on capacitors in parallel make up the total charge Q. Also, we know that the equivalent capacitance of two capacitors in parallel is the sum of two capacitances:

$$C=C_1+C_2.$$

Thus:

$$Q=V_2(C_1+C_2),\\ V_1C_1=V_2C_1+V_2C_2,\\ C_2=C_1\frac{V_1-V_2}{V_2}=3\text{ F}.$$