11.3 Capacitance

The diagram shows a diode bridge rectification circuit and a load resistor.

The input is a sinusoidal signal. Which of the following circuits will produce the smoothest output signal?

Three capacitors, each one with a capacitance C, are connected such that their combined capacitance is 1.5C. How are they connected?

A variable capacitor is being charged, but the dial is accidentally knocked partway through the charging process. 

What is the energy stored in this capacitor by the time the accumulated charge reaches 2.0 μC?

A capacitor with capacitance C discharges through a resistor of resistance R. The graph shows the variation with time t of the voltage V across the capacitor. 

The capacitor is now changed to one with a capacitance of 2C and the resistor is changed to one with a value of 2R. Which graph shows the variation of V with t when the new configuration is discharged. 

Which of the following can be used as a unit for capacitance? 

A parallel–plate capacitor has square plates of length L separated by a distance 3L and is filled with air as its dielectric.

A second capacitor has square plates of length 3L separated by distance 6L and is filled with a different dielectric.

Both capacitors have the same capacitance.

What is the relative permittivity of the dielectric in the second capacitor?

A capacitor of capacitance C stores an amount of energy E when the pd across it is V. 

Which line, A to D, in the table gives the correct stored energy and pd when the charge is decreased by 60%?

An uncharged 200 nF capacitor is connected to a power supply and becomes fully charged. The potential difference across the capacitor is equal to 9.0 V and the load resistor has a resistance of 2.0 kΩ.

A switch is flipped and a highly precise digital data logger begins recording information about the capacitor at the exact moment that the capacitor begins discharging. 

Approximately how many additional electrons are left on the negative plate after 0.60 ms have passed?

The following table of logarithm approximations may help you answer this question. 

Switch S in the circuit is held in position 1, so that the capacitor C becomes fully charged to a potential difference V and stores energy E.

The switch is then moved quickly to position 2, allowing C to discharge through the fixed resistor R. It takes 55 ms for the pd across C to fall to .

What period of time must elapse, after the switch has moved to position 2, before C has lost ?

Energy stored in between the plates of parallel plate capacitor of area A with a permittivity of the dielectric between the plates ε, electric field strength E and separated by distance $d$ is given by

The capacitance of a pixel of a CCD is 6.4 pF. A pulse of light is incident on the pixel and as a result, 10⁶ electrons are ejected from the pixel. The magnitude of the change in potential of the pixel is

A parallel-plate capacitor is connected to a cell of constant emf. The separation between the plates is doubled without disconnecting the cell. What are the changes in the energy stored in the capacitor, the magnitude of the capacitance of the capacitor and the charge stored on the plates?

The circuit below shows 4 capacitors each with capacitance 2.0 mF.

The total energy stored in the circuit is 100 J. What is the value of V?

A capacitor is charged by a constant current of 5.0 μA for 2 minutes. As a result, the potential difference across the capacitor increases by 10 V.

What is the capacitance of the capacitor?

Four capacitors of same capacitance are connected in parallel. When they are connected to a cell, a total charge of 2$.4\mu C$ is accumulated on them. After discharging, they are connected in series and then charged by the same cell.

What is the total charge stored on the capacitors after charging in series?

Three capacitors are connected in series with capacitances 6 µF, 3 µF and 4 µF respectively.

What is the combined capacitance of these capacitors?

Two capacitors of different capacitance are connected in series to a source of emf with negligible internal resistance.

What is correct about the potential difference across each capacitor and the charge on each capacitor?

A capacitor of capacitance C discharges through a resistor of resistance R. The graph shows the variation with time t of the voltage V across the capacitor.

The capacitor is changed to one of value  and the resistor is changed to one of value . Which graph shows the variation with t of V when the new combination is discharged?