Dielectrics and Capacitance Questions and Answers

Answer: C

In a series arrangement the flux density is common and the field intensity differs, being inversely proportional to permittivity. The other three statements correctly describe what is shared in each of the two configurations.

Answer: D

The field bulges outward beyond the edges, so more flux passes than the plane parallel picture allows and the capacitance is higher. The effect is small when the plates are large compared with their spacing, and guard rings are used when it must be eliminated for a precise measurement.

Answer: A

In a plain cable the field is greatest at the conductor surface and falls outward, so the outer material is under-used. Higher permittivity next to the conductor lowers the field there and raises it further out, allowing thinner insulation for the same working voltage.

Answer: B

Energy at constant voltage is proportional to capacitance, which is proportional to permittivity, so the factor is five. At constant charge instead the energy would fall to a fifth, which is the opposite result and shows why the constraint must always be stated.

Answer: C

The two-wire arrangement is closely analogous to the coaxial one, both giving a logarithmic result because the field of a line charge falls as the inverse first power. This is why line capacitance changes only slowly as conductors are spaced further apart.

Answer: D

Correct answer: 35.4 nC/m\( ^2 \)

\[ P = \epsilon_0(\epsilon_r-1)E = 8.854\times10^{-12} \times 4 \times 1000 = 3.54\times10^{-8}\ \mathrm{C/m^2} = 35.4\ \mathrm{nC/m^2}. \] The subtraction of one is what is easily forgotten: using \( \epsilon_r \) itself gives 44.3 nC/m², which is offered here, and would be the flux density rather than the polarisation.

Answer: A

The molecules cannot turn fast enough to follow a rapidly reversing field, so their contribution drops out and the permittivity falls from about eighty at low frequency toward the value set by electronic polarisation alone. The energy absorbed during that relaxation is what heats food in a microwave oven.

Answer: B

Electronic polarisation distorts the electron cloud, ionic polarisation displaces ions within the lattice, and orientational polarisation turns molecules that already possess a dipole moment. Each responds up to a different frequency, which is why permittivity falls in steps as frequency rises.

Answer: C

The thickness of the dielectric and its strength together fix the voltage the capacitor withstands, while the area and permittivity fix the capacitance. The two requirements pull against each other, since a thicker dielectric reduces the capacitance for a given area.

Answer: D

Equal capacitances give an equal division, so each sees half the total. In practice a slight mismatch in leakage resistance can make the division unequal on direct voltage, which is why balancing resistors are fitted across each unit of a high voltage series string.