Capacitance: Practice Questions

A capacitor has a capacitance of \(4.7\text{ }μ\text{F}\) and is charged to a potential difference of \(12\text{ V}\). What is the magnitude of the charge stored on either plate of the capacitor?

A capacitor is charged to a potential difference \(V_0\) and stores energy \(E_0\). If the potential difference across the capacitor is increased such that the stored energy becomes \(4E_0\), by what factor does the charge stored on the capacitor increase?

A \(20\text{ }μ\text{F}\) capacitor is charged to a potential difference of \(50\text{ V}\) and then disconnected from the power supply. It is then connected in parallel with an uncharged \(30\text{ }μ\text{F}\) capacitor. What is the total energy dissipated as heat and radiation during the redistribution of charge?

A capacitor stores a charge of \(3.0 \times 10^{-4}\text{ C}\) when connected across a \(15\text{ V}\) power supply. What is the electrical energy stored in the capacitor?

Two capacitors of capacitance \(6.0\text{ }μ\text{F}\) and \(12.0\text{ }μ\text{F}\) are connected in series across a \(9.0\text{ V}\) d.c. supply. What is the potential difference across the \(6.0\text{ }μ\text{F}\) capacitor?

A parallel-plate capacitor is charged such that the potential difference across its plates is \(12.0\text{ V}\). The charge stored on each plate is \(4.80\times 10^{-5}\text{ C}\).
(a) Calculate the capacitance \(C\) of the capacitor.
(b) Determine the energy stored in the capacitor.

A capacitor \(C_1 = 6.0\,\mu\text{F}\) is charged to a potential difference of \(50.0\text{ V}\) and then isolated from the power supply. It is then connected in parallel with an uncharged capacitor \(C_2 = 4.0\,\mu\text{F}\).
(a) State the total charge conserved in the system.
(b) Calculate the common potential difference \(V_f\) across the parallel combination.
(c) Calculate the loss in total electrostatic energy stored in the capacitors after connection.