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A-LEVEL 9702 · A2 · TOPIC 19
Capacitance and the capacitor .
The chain of the topic: a capacitor stores charge in proportion to potential, C = Q/V; building the charge against a rising voltage stores energy equal to the area under the V–Q graph; and letting that charge drain through a resistor gives the exponential decay set by the time constant τ = RC. Around the hexagon are the three ideas; above is what it builds on, below is where it leads.
TOPIC 19: CAPACITANCE
CAMBRIDGE A-LEVEL PHYSICS 9702 · PATHWAYS
TheLucidSTEM · thelucidstem.com
BUILDS ON
T9 Charge, current, p.d. T10 D.C. circuits and R T18 Electric fields: potential and energy 19.1
19.1
19.2
19.3
TOPIC 19
CAPACITANCE
1 · CAPACITORS AND CAPACITANCE
Charge stored per unit potential.
Two plates hold equal and opposite charge ±Q.
Capacitance C = Q/V, measured in farads (C V−¹).
Parallel adds C; series adds 1/C, like resistors swap.
C = Q / V
Cₚ = C₁+C₂+... 1/Cₛ = 1/C₁+1/C₂+...
+Q
−Q
potential difference V across the gap
2 · ENERGY STORED
Work done charging it up against V.
As charge builds, the next bit needs more work.
Energy W = area under the V against Q graph.
Triangle area gives the factor of one half.
W = ½QV = ½CV² = ½Q²/C
V
Q
W = area
slope of the line is 1/C
3 · DISCHARGING: THE TIME CONSTANT
Charge drains through R, ever more slowly.
Current I = V/R falls as V falls, so decay slows.
Time constant τ = RC: time to fall to 1/e (about 37%).
V, Q and I all decay with the same exponential.
x = x₀ e^(−t/RC) τ = RC
V
t
V₀
τ
0.37V₀
4 · THE RC CIRCUIT AT WORK
One capacitor, one resistor, one switch.
Close to the source: C charges toward the supply V.
Switch to R alone: C discharges through R.
Larger R or C gives a longer τ, so slower change.
I = I₀ e^(−t/RC), I₀ = V₀/R
C
R
I
capacitor discharging through R
LEADS TO
T21 Alternating currents: smoothing capacitors after rectifying T20 Magnetic fields: energy storage and timing circuits T18 Electric fields: revisit field and potential in the gap The same idea recurs: stored charge and the time constant τ = RC set how fast electronic systems respond and smooth.
← Builds on IGCSE: Circuits & charge