At a conductor to dielectric boundary, the tangential field in the dielectric is
Answer: C
The conductor surface is an equipotential, so no tangential field can exist just outside it either, the tangential component being continuous. The normal component is fixed by the surface charge density divided by the permittivity of the dielectric.
Please log in or register to report this question.
Capacitance is defined as the ratio of
Answer: D
Correct answer: charge to potential difference
\[ C = \frac{Q}{V}, \] measured in farads. It is a property of the geometry and the dielectric, not of the charge or voltage applied, so a capacitor has the same capacitance whether it is charged or not. Energy over voltage and energy over charge are different quantities entirely.
Please log in or register to report this question.
The capacitance of a parallel plate arrangement is
Answer: A
A larger area holds more charge at a given voltage and a smaller separation gives a stronger field for the same voltage, so the capacitance rises in both cases. The formula neglects fringing at the edges, which makes the true value slightly larger.
Please log in or register to report this question.
The capacitance per unit length of a coaxial cable depends on the two radii through
Answer: B
Integrating the inverse first power field between the conductors produces a logarithm, so the capacitance per unit length is \( 2\pi\epsilon/\ln(b/a) \). Because the dependence is logarithmic, quite large changes in the radii alter the capacitance rather little.
Please log in or register to report this question.
The capacitance of an isolated conducting sphere of radius \( a \) is
Answer: C
It follows from the potential of a sphere by rearrangement, and it may be read as the limit of two concentric spheres as the outer one recedes to infinity. A sphere of one metre radius has about 111 picofarads, which shows how small an isolated capacitance is.
Please log in or register to report this question.
Capacitors connected in parallel have a combined capacitance equal to
Answer: D
Each carries the same voltage and contributes its own charge, so the charges add and the ratio of total charge to voltage is the sum of the capacitances. Physically it amounts to increasing the plate area, which the formula for a parallel plate capacitor confirms.
Please log in or register to report this question.
When several capacitors are joined so that the same charge passes through each in turn, the combined value is
Answer: A
The same charge appears on each and the voltages add, so the reciprocals combine. The result is always smaller than the smallest member, which is the counterpart of resistances in parallel and the reason a series string is used to share a high voltage.
Please log in or register to report this question.
Inserting a dielectric slab that fills the space between the plates of a capacitor
Answer: B
For the same voltage the polarised medium allows more charge to be held, so the capacitance rises in proportion to the permittivity. This is the main reason dielectrics are used at all, the second being mechanical separation of the plates.
Please log in or register to report this question.
A parallel plate capacitor is half filled with a dielectric slab covering the whole area but only half the gap. The arrangement behaves as
Answer: C
The same flux passes through both layers in turn, so the voltages across them add and the capacitances combine as a series pair. Had the slab covered half the area over the whole gap the combination would have been parallel instead.
Please log in or register to report this question.
A parallel plate capacitor has a dielectric slab covering half its area over the whole gap. The arrangement behaves as
Answer: D
Both parts see the same voltage across the same gap, so their charges add and the capacitances add. Recognising whether a composite arrangement is series or parallel comes down to asking whether the voltage or the flux is shared.
Please log in or register to report this question.
