On the axes, draw a graph to show the variation with time of the voltage across the resistor.

(i) The time constant of this circuit is 22s. State what is meant by the time constant.

(ii) Calculate the resistance R.

A dielectric material is now inserted between the plates of the fully charged capacitor. State the effect, if any, on

(i) the potential difference across the capacitor.

(ii) the charge on one of the capacitor plates.

(i) The permittivity of the dielectric material in (c) is twice that of a vacuum. Calculate the energy stored in the capacitor when it is fully charged.

(ii) The switch in the circuit is now moved to position B and the fully charged capacitor discharges. Describe what happens to the energy in (d)(i).

(i)
the time for the voltage/charge/current «in circuit» to drop to \(\frac{1}{e}\) or 37% of its initial value

«as the capacitor discharges»

OR

time for voltage/charge/current «in circuit» to increase to \(\left( {1 - \frac{1}{e}} \right)\) or 63% of its final value

«as the capacitor charges»

(ii)
\(R =  \ll \frac{{22}}{{4.5 \times {{10}^{ - 6}}}} =  \gg 4.9 \times {10^6}\Omega \)

(i)
no change
OR
«remains at» 12 V

(ii)
increases
OR
doubles

(i)
recognises that new capacitance is 9.0 μF

\(E =  \ll \frac{1}{2}C{V^2} = \frac{1}{2} \times 9.0 \times {10^{ - 6}} \times {12^2} \gg  = 0.65{\rm{mJ}}\) or 6.5×10^–4J

Allow 11.8 V (value on graph at t=100s).

(ii)
energy goes into the resistor/surroundings
OR
«energy transferred» into thermal/internal energy form

Do not accept “dissipated” without location or form.
Do not allow “heat”.