Dielectrics and Capacitance Questions and Answers

Answer: B

The combined capacitance is fifty picofarads and multiplying by two hundred volts gives \( 10^{-8} \) coulombs. Each capacitor carries its own share in proportion to its capacitance, four and six nanocoulombs respectively.

Answer: C

Dividing gives \( 11 \times 10^{3}/(20 \times 10^{6}) = 5.5 \times 10^{-4} \) m. In practice a factor of several times this would be used, to allow for voids, ageing, surges and the reduction of strength with time under stress.

Answer: D

With the charge fixed and the capacitance trebled, the voltage must fall to a third. The stored energy falls to a third as well, the difference having been given up as mechanical work as the slab was drawn into the gap.

Answer: A

With the voltage fixed and the capacitance trebled, the charge must treble too and the source supplies the extra. The stored energy also trebles, and the source in fact delivers twice that increase, half of it being dissipated or done as work.

Answer: B

Capacitance is the ratio of charge to voltage and both rise together, so the ratio is fixed by geometry and permittivity alone. Only if the dielectric is nonlinear, as some ferroelectric ceramics are, does the capacitance depend on the applied voltage.

Answer: C

Correct answer: False, bound charge being unable to move through the dielectric to earth

Bound charge is not free to move: it belongs to molecules held in place, and an earth connection has nothing to conduct. That is exactly what distinguishes it from the free charge on a conductor, which an earth wire removes at once. The bound charge disappears only when the field that produced the polarisation is removed.

Answer: D

It is the normal flux density that is continuous when no free surface charge is present; the field intensity jumps in inverse proportion to the permittivities. The tangential intensity is the component that is always continuous.

Answer: A

The reciprocals add, so the reciprocal of the total exceeds each individual reciprocal and the total is smaller than the smallest member. When one is much larger than the other the total tends to the smaller one but never exceeds it.

Answer: B

The flux density is continuous across the void, so the field there is higher by the ratio of the permittivities, and air is weaker than the solid besides. Both effects act the same way, which is why voids are the chief enemy of high voltage insulation.

Answer: C

The polarisation charge on the faces of the slab acts like a pair of oppositely charged sheets whose field opposes the applied one. The reduction is by the factor of the relative permittivity, and it is exactly why a dielectric raises the capacitance.