A parallel-plate capacitor is charged and then disconnected from the supply. Which of the following will increase the capacitance of the capacitor?

An air-filled capacitor C consists of two parallel plates, each of area A and separated by a distance d. A dielectric with relative permittivity 5 is then inserted between the two plates. What is the new capacitance of the capacitor?

A capacitor is charged by a constant current of 4.0 mA for 0.80 s. If the potential difference across the capacitor is 320 V, what is the capacitance of the capacitor?

A parallel-plate capacitor of cross-sectional area A is connected across a battery of potential difference V. A dielectric is then inserted into the capacitor. If the relative permittivity of the dielectric is 2.5 and the distance of separation between the plates is 0.050 mm, calculate the ratio of charge on the capacitor without the dielectric to the charge on the capacitor with dielectric.

Two uncharged capacitors of capacitance 2.0 $\mu F$  and 4.0 $\mu F$  are connected in parallel with a battery of e.m.f., E and negligible resistance as shown in the diagram. After 20 s, the ammeter reads 3.0 $\mu A$  . What is the value of e.m.f.E?

A capacitor is connected in series with a light bulb and a voltage supply as shown in the diagram. If a dielectric is inserted between the parallel plates of the capacitor, which statement is not true about the capacitor?

An uncharged capacitor of capacitance 8.0 $\mu F$  is connected to a battery of e.m.f. V and negligible internal resistance. If the charge on each plate of the capacitor is 24 $\mu C$  , what is the value of V?

Nine capacitors are arranged in a circuit as shown in the diagram. Which section of the circuit provides the lowest capacitance?

Two capacitors of capacitance 3 $\mu F$  and 2 $\mu F$  are connected in series with the battery as shown in the diagram. If  $V_1$  and  $V_2$  are the potential difference across the capacitors of  3 $\mu F$  and 2 $\mu F$  respectively, what is the ratio of  $\frac{V_1}{V_2}$  ?

A capacitor of capacitance 60 pF is charged to a potential difference of 400 v. Calculate the energy stored in the capacitor.

A charged capacitor consists of two parallel plates, each of area 0.500  $m^2$  and separated by a distance of 9.00 mm. If the electric field strength between the plates is 3.0 $\times10^6$  V $m^{-1}$  , calculate the energy stored in the capacitor.

A charged capacitor of capacitance 3 $\mu F$  is connected to a resistor of resistance  $10^6$   $\Omega$  . Find the fraction of energy stored in the capacitor after 1.0 s.

Three Charged capacitors each of capacitance C are connected to three resistors each of resistance R as shown in the diagram. When switch S is closed, calculate the time constant of the circuit.

A capacitor with charge Q is connected across a resistor for 76 s. The charge on the capacitor decreases to 5.0 $\times$  $10^{-4}$  times its initial charge. Calculate the time constant of the circuit.

A charged capacitor is connected to a filament bulb. The time constant of the circuit is $\tau$ . The filament bulb is replaced with another filament bulb which has the same material and cross-sectional area for its filament wire but double the length. What is the time constant of the new circuit?