Interpret capacitor discharge graphs
Read how potential difference, charge and current change with time as a capacitor discharges through a resistor.
A Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 19. These original explanations and calculations are study aids; full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use charge, potential difference, current, resistance, graph area, energy and SI units.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
During passive discharge through a resistor, what happens to the capacitor's charge magnitude?
What you will learn
- Analyse time graphs for discharging potential difference
- Analyse time graphs for capacitor charge and current
- Relate initial gradient and long-term behavior to discharge
Charge and voltage fall during discharge
When a charged capacitor discharges through a resistor, its charge magnitude and potential-difference magnitude decrease towards zero. Their time graphs are exponential: the fall is steepest initially and then becomes more gradual.
For a fixed capacitor, Q = CV, so Q and V have the same normalized decay shape and the same time constant. They approach zero asymptotically in the ideal model rather than reaching it at a finite time.
Current magnitude decays as the discharge slows
The current magnitude is initially greatest because the potential difference across the resistor is largest. As Q and V fall, current magnitude also decreases towards zero with the same exponential time constant for a simple resistor–capacitor circuit.
A chosen current reference direction may make the signed discharge current negative. State whether a graph shows current magnitude or signed current; the magnitude decreases from its initial value while the signed value approaches zero from its chosen side.
Pause and explain
Which graph feature indicates exponential rather than constant-rate discharge?
Worked example
Sketch in words the charge–time graph for a capacitor discharging through a resistor from initial charge Q₀.
Show the worked solution
- Identify the initial value and long-time limit.
- Use the exponential discharge shape.
- Compare the rate of change at early and later times.
Answer Q starts at Q₀, falls rapidly at first, then more slowly, and approaches zero asymptotically.
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Compare the charge and potential-difference graphs for a capacitor discharging through a fixed resistor.
Give me a hint
Use Q = CV with constant C.
Compare my reasoning
- Q is proportional to V for fixed capacitance.
- Both quantities start at their initial values and fall exponentially.
- Their normalized graphs have the same time constant and both approach zero.
Charge and potential difference share the same normalized exponential decay shape and time constant.
Look for these in your work
- Proportionality recalled
- Decay behavior stated
- Time constant comparison made
A signed current graph starts at −0.80 mA and approaches zero during discharge. Has the current magnitude increased or decreased?
Give me a hint
Compare absolute values, not just the signed numbers.
Compare my reasoning
- Initial magnitude is 0.80 mA.
- As the signed value approaches zero, its absolute value becomes smaller.
- The current magnitude decreases.
The current magnitude decreases from 0.80 mA towards zero.
Look for these in your work
- Initial magnitude identified
- Sign distinguished from magnitude
- Trend stated
A capacitor's voltage falls from 10 V to 6.0 V in the first time interval, then from 6.0 V to 3.6 V in an equal interval. What does this suggest about its discharge graph?
Give me a hint
Compare fractional changes over equal times.
Compare my reasoning
- The first ratio is 6.0/10 = 0.60.
- The second ratio is 3.6/6.0 = 0.60.
- Equal-time intervals with a common remaining fraction are consistent with exponential decay.
The repeated 0.60 fraction per equal interval is consistent with an exponential discharge curve.
Look for these in your work
- Ratios calculated
- Equal intervals compared
- Exponential pattern inferred
Common mistakes
- Drawing a straight-line decrease for exponential discharge
- Showing charge or voltage growing during passive discharge
- Claiming current remains constant
- Confusing signed current with current magnitude
What can you explain now?
During passive discharge through a resistor, what happens to the capacitor's charge magnitude?
Compare with the explanation
It decreases towards zero
Charge leaves the capacitor through the resistor.
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Make it stick
How do the capacitor's voltage, charge and current graphs behave during discharge?
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