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Creating Models

Charging a capacitor

  • 3 things to know
  • Components 01, 02 and 03

Overview

Recall questions on Q = Q₀(1 − exp(−t/RC)) and V = V₀(1 − exp(−t/RC)), the 63% stored after one time constant, why the charging current falls and I = I₀exp(−t/RC), current–time graphs for charging and discharging, time constant and potential difference calculations, the resistor and capacitor potential differences, series resistance, and stored energy.

What you need to know

Answer each one before you reveal it.

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Key term

What equation gives the charge on a capacitor being charged through a resistor?

Key term

What fraction of the final charge is on a capacitor after one time constant of charging?

Key term

Why does the charging current fall as the capacitor charges?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What equation gives the charge on a capacitor being charged through a resistor?

    Model answer

    The charge is Q = Q₀(1 − exp(−t/RC)), where Q₀ is the final charge.

  2. 2

    Describe the shape of a graph of potential difference against time as a capacitor charges.

    Model answer

    It rises steeply from zero, curves over and approaches the supply potential difference asymptotically.

  3. 3

    What fraction of the final charge is on a capacitor after one time constant of charging?

    Model answer

    About 0.63, since 1 − e⁻¹ = 0.63, so 63% of the final charge is stored.

  4. 4

    Why does the charging current fall as the capacitor charges?

    Model answer

    The growing potential difference across the capacitor opposes the supply, so the potential difference across the resistor and hence the current both fall.

  5. 5

    What is the expression for the current during the charging of a capacitor?

    Model answer

    The current is I = I₀exp(−t/RC), with I₀ = V₀/R at the instant charging begins.

  6. 6

    Describe the shape of the current–time graph for a charging capacitor.

    Model answer

    It starts at its maximum value and decays exponentially towards zero.

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