Six identical capacitors, each of value C, are connected as shown.

What is the total capacitance?

A. $\frac{C}{6}$

B. $\frac{2C}{3}$

C. $\frac{3C}{3}$

D. 6C

The capacitor is fully charged and the space between the plates is then filled with a dielectric of permittivity ε = 3.0ε₀.

Explain whether the magnitude of the charge on plate A increases, decreases or stays constant.

The capacitor is connected to a 16 V cell as shown.

Calculate the magnitude and the sign of the charge on plate A when the capacitor is fully charged.

State one assumption that needs to be made so that the Earth-thundercloud system may be modelled by a parallel plate capacitor.

Calculate the final total energy, in J, stored in X and Y.

The resistor R in the circuit has a resistance of 1.2 kΩ. Calculate the time taken for the charge on the capacitor to fall to 50 % of its fully charged value.

Show that about –11 C of charge is delivered to the Earth’s surface.

Three identical capacitors are connected in series. The total capacitance of the arrangement is $\frac{1}{9}$mF. The three capacitors are then connected in parallel. What is the capacitance of the parallel arrangement?

A. $\frac{1}{3}$mF   

B. 1 mF

C. 3 mF

D. 81 mF

Calculate the change in the energy stored in the capacitor.

Suggest why the answers to (a) and (b)(ii) are different.

The circuit diagram shows a capacitor that is charged by the battery after the switch is connected to terminal X. The cell has emf V and internal resistance r. After the switch is connected to terminal Y the capacitor discharges through the resistor of resistance R.

What is the nature of the current and magnitude of the initial current in the resistor after the switch is connected to terminal Y?

Four identical capacitors of capacitance X are connected as shown in the diagram.

What is the effective capacitance between P and Q?

A.   $\frac{\text{X}}{3}$

B.   X

C.   $\frac{\text{4X}}{3}$

D.   4X

Calculate in V, the potential difference between the thundercloud and the Earth’s surface.

Show that the capacitance of this arrangement is C = 6.6 × 10^–7 F.

Calculate the maximum charge Q₀ stored in the capacitor.

Show that the charge remaining in the capacitor after a time equal to one time constant $\tau$ of the circuit will be 0.37 Q₀.

The graph shows the variation with time of the charge in the capacitor as it is being discharged through the heart.

Determine the electrical resistance of the closed circuit with the switch in position B.

Show that the maximum energy stored by the capacitor is about 160 J.

A capacitor of capacitance X is connected to a power supply of voltage V. At time t = 0, the capacitor is disconnected from the supply and discharged through a resistor of resistance R. What is the variation with time of the charge on the capacitor?

$\text{A. }\frac{X}{V}{e}^{-RXt}$

$\text{B. }\frac{X}{V}{e}^{-\frac{t}{RX}}$

$\text{C. }XV{e}^{-RXt}$

$\text{D. }XV{e}^{-\frac{t}{RX}}$

Calculate the final charge on X and the final charge on Y.

The motor can transfer one-third of the electrical energy stored in the capacitor into gravitational potential energy of the mass. Determine the maximum height through which a mass of 45 g can be raised.

A capacitor is charged with a constant current $I$. The graph shows the variation of potential difference $V$ across the capacitor with time $t$. The gradient of the graph is $G$. What is the capacitance of the capacitor?

A.  $\frac{I}{G}$

B.  $\frac{G}{I}$

C.  $G\times I$

D.  $\frac{1}{G\times I}$

A capacitor of capacitance $C$ has initial charge $Q$. The capacitor is discharged through a resistor of resistance $R$. The potential difference $V$ across the capacitor varies with time.

What is true for this capacitor?

A.  After time $\frac{RC}{2}$ the potential difference across the capacitor is halved.

B.  The capacitor discharges more quickly when the resistance is changed to $2R$.

C.  The rate of change of charge on the capacitor is proportional to $V$.

D.  The time for the capacitor to lose half its charge is $\frac{\ln 2}{RC}$.

The capacitance of the capacitor is 22 mF. Calculate the energy stored in the capacitor when it is fully charged.

The resistance of the wire is 8.0 Ω. Determine the time taken for the capacitor to discharge through the resistance wire. Assume that the capacitor is completely discharged when the potential difference across it has fallen to 0.24 V.

Calculate in J, the energy stored in the system.

Calculate the distance between the plates.

The cell is used to charge a parallel-plate capacitor in a vacuum. The fully charged capacitor is then connected to an ideal voltmeter.

The capacitance of the capacitor is 6.0 μF and the reading of the voltmeter is 12 V.

Calculate the energy stored in the capacitor.

Calculate the total length of aluminium foil that the student will require.

Two initially uncharged capacitors X and Y are connected in series to a cell as shown.

What is $\frac{\text{voltage across X}}{\text{voltage across Y}}$?

A.  $\frac{1}{2}$

B.  $1$

C.  $2$

D.  $4$

The switch is then connected to Y and C discharges through the 20 MΩ resistor. The voltage V_c drops to 50 % of its initial value in 5.0 s. Determine the capacitance of C.

Show that the charge stored on C₁ is about 0.04 mC.

Explain why the energy gained by capacitor C₂ differs from your answer in (b)(i).

Calculate the energy transferred from capacitor C₁.