Me

Discharging a capacitor Edexcel International A Level Physics revision

Not started

Learn it

In plain words

Let a charged capacitor empty through a resistor and it starts fast and gets slower and slower, like a bath draining as the water level drops. In each equal stretch of time it loses the same fraction of what is left. That pattern is called exponential decay.

4 things to know

  1. When a capacitor discharges through a resistor, its charge, its p.d. and the current all fall exponentially: Q = Q₀e^(−t/RC), and the same for V and I.
  2. The time constant is RC, in seconds. It is the time for the charge (or the p.d., or the current) to fall to 1/e of its starting value, which is about 37%.
  3. On a graph against time, each quantity falls steeply at first and then more and more gently, never quite reaching zero.
  4. Taking logs gives ln Q = ln Q₀ − t ÷ RC. So a graph of ln Q (or ln V, or ln I) against t is a straight line with gradient −1 ÷ RC.

Worked example

A 100 µF capacitor charged to 12 V discharges through a 50 kΩ resistor. Find the time constant, and the p.d. after 10 s.

  1. Time constant = RC = 50 × 10³ × 100 × 10⁻⁶ = 5.0 s.
  2. V = V₀e^(−t/RC) = 12 × e^(−10 ÷ 5.0) = 12 × e⁻².
  3. = 12 × 0.135 = 1.6 V.

Tips and tricks

  • With R in ohms and C in farads, RC comes out in seconds.
  • After one time constant 37% is left; after two, about 14%; after five, less than 1%.
5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Discharging a capacitor: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. What is the time constant of a capacitor discharging through a resistor?
    • RC (the answer)
    • R ÷ C
    • C ÷ R
    • 1 ÷ RC

    A bigger resistance or a bigger capacitance gives a slower discharge.

  2. What fraction of its charge is left on a capacitor after one time constant?
    • 14%
    • 37% (the answer)
    • 50%
    • 63%

    1 ÷ e is 0.37.

  3. The resistance a capacitor discharges through is doubled. What happens to the time it takes to discharge?
    • It doubles. (the answer)
    • It halves.
    • It stays the same.
    • It becomes four times longer.

    The time constant RC doubles.

  4. What does a graph of ln V against t look like for a discharging capacitor?
    • a straight line sloping downwards (the answer)
    • a curve that levels off
    • a horizontal line
    • a straight line sloping upwards

    Its gradient is −1 ÷ RC.

  5. A capacitor charged to 10 V begins to discharge through a 2 kΩ resistor. What is the current at the start?
    • 0.2 mA
    • 5 mA (the answer)
    • 20 mA
    • 20 A

    I = V ÷ R at that instant.

Things you can type

Or go straight to

Or browse a shelf