Title: InkPhysics / Capacitance
On every note of this deck, unless a note says otherwise:
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Front: RECALL
State how to find the energy stored from a pd-charge graph.
Back: The energy stored is the area under the graph of pd against charge, ½QV.

Front: SPOT THE ERROR
Say what is wrong with this claim: After one time constant the capacitor is empty.
Back: After one time constant the charge has fallen to 1/e, about 37%, of its initial value, not zero. Each further time constant loses the same fraction, so it never quite empties.

Front: SPOT THE ERROR
Say what is wrong with this claim: A capacitor charges at a steady rate until it is full.
Back: Charging is exponential, not steady. As charge builds, the capacitor's pd rises and the pd driving the current falls, so the charging current decays; it never becomes strictly full.

Front: RECALL
Explain why capacitors in series all carry the same charge.
Back: The conductor running between the facing plates of two series capacitors is isolated, and it started neutral, so charge is conserved on it: the charge drawn onto one plate leaves an equal and opposite charge on the next. (CIE and OCR only.)

Front: RECALL
State how to find current from a charge-time graph.
Back: The current is the magnitude of the gradient of the charge-time graph. On discharge that gradient is negative, the minus sign meaning charge is leaving the plates.

Front: RECALL
State the effect of doubling the pd on the energy stored.
Back: The energy quadruples, since E = ½CV^2.

Front: RECALL
State the combined capacitance of capacitors in parallel.
Back: C = C_1 + C_2 + …, because every capacitor takes the same pd and their charges add. The result is always larger than the largest capacitor in the group. (CIE and OCR only.)

Front: RECALL
State what Q means for a charged capacitor.
Back: Q is the magnitude of the charge on one plate; the capacitor as a whole is neutral.

Front: DEFINITION
Define: Capacitance.
Back: The charge stored per unit potential difference: C = Q/V, in farads.

Front: RECALL
State the shape of the three discharge graphs.
Back: Charge, pd and current all fall along the same exponential decay curve.

Front: RECALL
State the unit of the time constant RC.
Back: Ohms times farads gives seconds.

Front: EQUATION · NOT ON THE DATA SHEET
Halving time for a discharging capacitor:
T_½ = ?\(T_{½} = \, ?\)T_½ = ?
Back: T_½ = 0.69RC\(T_{½} = 0.69RC\)T_½ = 0.69RC

Front: RECALL
State the gradient of a ln V against t discharge graph.
Back: The gradient is −1/RC, so the time constant is the negative reciprocal of the gradient.

Front: RECALL
State the initial current when a capacitor charges through a resistor.
Back: I_0 = V/R, because the uncharged capacitor has no pd and the full supply pd sits across the resistor.

Front: RECALL
State the effect of a dielectric on capacitance.
Back: A dielectric of relative permittivity ε_r multiplies the capacitance by ε_r.

Front: RECALL
State how to find charge from a current-time graph.
Back: The charge transferred is the area under the current-time graph.

Front: RECALL
State which capacitor in a series pair takes the larger pd.
Back: The smaller one. Both hold the same charge, and V = Q/C, so the poorer rating needs more volts to hold it. This is the reverse of a series resistor chain. (CIE and OCR only.)

Front: RECALL
State the capacitance of an isolated spherical conductor.
Back: C = 4πε_0r, from C = Q/V with V = Q/(4πε_0r), the potential measured from zero at infinity. It depends on the radius alone. (CIE only.)

Front: RECALL
State the combined capacitance of capacitors in series.
Back: 1/C = 1/C_1 + 1/C_2 + …, because every capacitor carries the same charge and their pds add. The result is always smaller than the smallest capacitor in the group. (CIE and OCR only.)

Front: RECALL
State the fraction of final charge reached one time constant after charging begins.
Back: 63%, the complement of the 37% left behind in discharge.

Front: DEFINITION
Define: Time constant.
Back: The time RC for the charge on a capacitor to fall to 1/e, about 37%, of its initial value.

Front: SPOT THE ERROR
Say what is wrong with this claim: A capacitor is a small battery.
Back: A battery is a source of emf, converting chemical energy at a near-steady voltage; a capacitor only stores separated charge, and its pd falls as soon as it discharges.