Capacitance · revision map · A-Level 9702, Topic 19

TOPIC 19 · CAPACITANCE
CAMBRIDGE INTERNATIONAL AS & A LEVEL PHYSICS 9702 · ONE-PAGE REVISION MAP
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CAPACITANCE19
Capacitors & Capacitance

A capacitor stores charge per unit potential. Two plates hold equal and opposite charge ±Q.

C = Q / V
unit farad (F)
1 F = 1 C V−¹

Combining capacitors (opposite to resistors):

parallel: C = C₁ + C₂ series: 1/C = 1/C₁ + 1/C₂ +Q −Q potential difference V across the gap
Energy Stored

Charging a capacitor does work against a rising voltage. Each extra bit of charge needs more work.

W = ½QV = ½CV² = ½Q²/C
  • Energy W = area under the V against Q graph.
  • The triangle area gives the factor of one half.
  • Slope of the V–Q line is 1/C.
V Q W = area
Discharging: The Time Constant

Charge drains through a resistor, ever more slowly: current I = V/R falls as V falls.

x = x₀ e^(−t/RC)
τ = RC
time to fall to
1/e (about 37%)
  • V, Q and I all decay with the same exponential.
  • Larger R or C gives a longer τ, so slower change.
V V₀ 0.37V₀ τ t
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)
initial current I₀ = V₀ / R
C R I C discharging through R
BUILDS ON · Electric fields · D.C. circuits · IGCSE circuits → CAPACITANCE → LEADS TO · Alternating currents · Magnetic fields
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