The charge on that same 10 \( \mu \)F capacitor at 100 V is
Answer: C
Multiplying gives \( 10^{-5} \times 100 = 10^{-3} \) coulombs. A millicoulomb is an enormous charge by electrostatic standards, which is why capacitor voltages of a hundred volts are ordinary while a charged sphere at a hundred volts holds almost nothing.
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Two dielectric layers of equal thickness and relative permittivities 2 and 4 fill a capacitor gap in series. The ratio of the fields in them is
Answer: D
The normal flux density is the same in both, so the field intensity is inversely proportional to the permittivity and is twice as large in the layer of permittivity two. That is where breakdown would begin, other things being equal.
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A 1 mm air gap lies in series with 4 mm of solid insulation of relative permittivity 4, across 1000 V. The field in the air gap is about
Answer: A
The equivalent electrical thickness of the solid is one millimetre, so the two layers behave as equal capacitances and share the voltage equally: 500 V across one millimetre of air, that is 500 kV/m. Air breaks down at about 3 MV/m, so this gap survives.
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A 20 pF capacitor and a 30 pF capacitor in parallel are charged to 200 V. The total charge stored is
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.
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The dielectric strength of a material is 20 MV/m. The minimum thickness for 11 kV, with no safety factor, is
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.
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A capacitor is charged and then disconnected, and a dielectric of relative permittivity 3 is inserted. The voltage across it becomes
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.
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If instead the capacitor stays connected to its source while the same dielectric is inserted, the charge on it becomes
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.
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True or false: the capacitance of an arrangement depends on the voltage applied to it.
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.
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True or false: bound charge in a dielectric can be conducted away by earthing the material.
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.
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True or false: the normal component of the electric field intensity is continuous across a dielectric boundary.
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.
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