Dielectrics and Capacitance Questions and Answers

Answer: C

The same current, and therefore the same charge, passes through both, so the voltages divide inversely with the capacitances and the smaller one takes almost all of it. On a direct supply the long-term division would instead be settled by the ratio of the leakage resistances, which is a quite different calculation.

Answer: D

The measured value is about 1.00059, so treating air as a vacuum introduces an error far smaller than that of any ordinary measurement. It does rise with pressure, which is why compressed gas capacitors and gas-insulated switchgear behave measurably differently from air-filled ones.

Answer: A

The product is \( 10^{-6} \times 10^{8} = 100 \) seconds, so the voltage falls to about a third in a minute and a half. This is why a large capacitor is fitted with a discharge resistor and why one should never assume a disconnected capacitor is safe to handle.

Answer: B

The area is \( 10^{-2} \) m², so \( 6 \times 8.854 \times 10^{-12} \times 10^{-2}/(5 \times 10^{-4}) = 1.06 \times 10^{-9} \) F. Mica capacitors of this construction were the standard precision component before plastic films displaced them.

Answer: C

The area appears in the numerator and the separation in the denominator, so doubling both cancels exactly. Recognising such a cancellation avoids recomputing the whole expression, and the same reasoning shows what happens when a capacitor is scaled up in every linear dimension at once.

Answer: D

The area grows as \( k^2 \) and the separation as \( k \), so the ratio grows as the first power of the scale. Capacitance therefore has the dimensions of a permittivity times a length, which is the same conclusion the isolated sphere formula reaches.

Answer: A

At constant voltage the energy is proportional to capacitance and so rises; at constant charge it is inversely proportional and so falls. In both cases the slab is drawn in, because the correct criterion at constant voltage includes the work done by the source and not merely the stored energy.

Answer: B

Substituting in \( \tfrac{1}{2}\epsilon_0\epsilon_r E^2 \) gives \( 0.5 \times 8.854 \times 10^{-12} \times 4 \times 10^{12} = 17.7 \) J/m³. Even at a megavolt per metre the density is modest, which is why electrostatic energy storage cannot compete with chemical storage on a volume basis.

Answer: C

The capacitance per unit area of a layer is the permittivity over the thickness, so equal values of thickness over permittivity means equal capacitances, and two equal capacitances in series divide the voltage equally. The fields in them differ, being inversely proportional to their permittivities.

Answer: D

Interleaved vanes must slide past one another repeatedly, which no solid dielectric would survive, and air introduces almost no loss at radio frequency. The penalty is a small capacitance for the volume, which is why such capacitors are physically large for a few hundred picofarads.