AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Capacitor charge and discharge (A-level only): Time constant RC.
The time constant of a capacitor–resistor circuit is the product of resistance and capacitance, τ = RC.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 4 of 5
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
The time constant of a capacitor–resistor circuit is the product of resistance and capacitance, τ = RC. It has units of seconds, because an ohm multiplied by a farad gives a second. During discharge, the charge, current and potential difference all fall exponentially, and after one time constant each quantity has fallen to 1/e of its initial value, about 37%. After about five time constants the values are close to zero. The time constant is the reciprocal of the exponential decay constant, so a larger R or a larger C gives a slower change. For charging, the capacitor reaches about 63% of its final value after one time constant. The time constant can be found from a graph by reading the time at which the value is 1/e of its starting value, or from the gradient of a graph of ln V against time, whose magnitude equals 1/RC.
What earns the marks
- States that the time constant τ = RC and that it has the unit of seconds.
- Explains that after one time constant a discharging quantity falls to 1/e of its initial value, approximately 37%, and a charging quantity rises to about 63% of its final value.
- Uses the exponential relationships, such as Q = Q₀e^(−t/RC) and V = V₀e^(−t/RC), to calculate a quantity at a given time or to find the time taken to reach a given value.
- Determines the time constant from a graph, for example by reading the time at which the value is 1/e of its initial value, or from the magnitude of the gradient of a straight-line graph of ln V against t.
- Explains that a larger resistance or a larger capacitance increases the time constant and therefore slows the charging or discharging process.
- Converts units correctly, for example microfarads to farads and kilohms to ohms, before multiplying to find RC.
Common mistakes and how to put them right
Treating the time constant as the time for the capacitor to become fully discharged.
Put it right: After one time constant the quantity has fallen only to about 37% of its initial value, and full discharge is approached only after several time constants.
Adding resistance and capacitance, or multiplying incorrectly, when finding the time constant.
Put it right: Use τ = RC with both values in SI units.
Using the natural logarithm of a ratio without the correct sign or base, for example confusing ln with log₁₀.
Put it right: Use natural logarithms consistently in the exponential decay relationship.
Exam tips
- Show the substitution into τ = RC with converted units, then state the answer in seconds.
- When reading a time constant from a graph, mark the 1/e value on the axis and draw across to the curve before reading the time.
- Link any calculated time constant to the physical behaviour, such as stating that the capacitor will take about five time constants to discharge almost completely.
Try the lesson
The start of the Capacitor charge and discharge (A-level only): Time constant RC. lesson, made from checked teaching notes for this specification point.
Have a go first
A capacitor of capacitance C discharges through a resistor of resistance R. Which expression gives the time constant of this circuit?
Listen
The time constant of a capacitor–resistor circuit is the product of resistance and capacitance, τ = RC. It has units of seconds, because an ohm multiplied by a farad gives a second. During discharge, the charge, current and potential difference all fall exponentially, and after one time constant each quantity has fallen to 1/e of its initial value, about 37%. After about five time constants the values are close to zero. The time constant is the reciprocal of the exponential decay constant, so a larger R or a larger C gives a slower change. For charging, the capacitor reaches about 63% of its final value after one time constant. The time constant can be found from a graph by reading the time at which the value is 1/e of its starting value, or from the gradient of a graph of ln V against time, whose magnitude equals 1/RC. A strong answer earns marks for these points. States that the time constant τ = RC and that it has the unit of seconds. Explains that after one time constant a discharging quantity falls to 1/e of its initial value, approximately 37%, and a charging quantity rises to about 63% of its final value. Uses the exponential relationships, such as Q = Q₀e^(−t/RC) and V = V₀e^(−t/RC), to calculate a quantity at a given time or to find the time taken to reach a given value. Determines the time constant from a graph, for example by reading the time at which the value is 1/e of its initial value, or from the magnitude of the gradient of a straight-line graph of ln V against t. A common slip: Treating the time constant as the time for the capacitor to become fully discharged. Instead, after one time constant the quantity has fallen only to about 37% of its initial value, and full discharge is approached only after several time constants. Exam tip: Show the substitution into τ = RC with converted units, then state the answer in seconds.
Key words
Say what each word means before you turn the card.
Time constant
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Exponential fall during discharge
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Determining the time constant from a graph
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Effect of larger R or C
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See every definition
- Time constant
- The product of resistance and capacitance, τ = RC, which has units of seconds because an ohm multiplied by a farad gives a second.
- Exponential fall during discharge
- During discharge, the charge, current and potential difference all fall exponentially, and after one time constant each quantity has fallen to 1/e of its initial value, about 37%.
- Determining the time constant from a graph
- Found by reading the time at which the value is 1/e of its starting value, or from the gradient of a graph of ln V against time, whose magnitude equals 1/RC.
- Effect of larger R or C
- A larger resistance or a larger capacitance increases the time constant and therefore slows the charging or discharging process.
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