AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Corresponding graphs for Q, V and I against time for charging and…
Full specification wording
Capacitor charge and discharge (A-level only): Corresponding graphs for Q, V and I against time for charging and discharging.
For a charging capacitor, Q and V both rise from zero towards maximum values, while I starts at its largest value and decays towards zero.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 2 of 5
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
For a charging capacitor, Q and V both rise from zero towards maximum values, while I starts at its largest value and decays towards zero. The Q and V curves have the same shape because Q = CV, so they are proportional. The current curve is also exponential but starts high, because at the first instant the capacitor has no p.d. and the supply p.d. is across the resistor. On discharge, Q, V and I all fall exponentially from their initial values towards zero, and I is in the opposite direction to the charging current. A reliable method is to write the initial value and the asymptote for each quantity, then sketch all three curves on the same time axis so their relationships are clear.
What earns the marks
- During charging, Q and V rise from zero and approach maximum values asymptotically.
- During charging, I starts at a maximum and decays towards zero.
- During discharging, Q, V and I all decay from their initial values towards zero.
- The Q and V graphs are proportional because Q = CV, so they have the same shape and the same time constant.
- The discharging current direction is opposite to the charging current direction.
- All three quantities share the same time constant τ = RC, so their graphs change at the same rate.
Common mistakes and how to put them right
Drawing the charging current curve as rising with the p.d. curve.
Put it right: The correct current curve starts at its maximum and decays.
Making the Q and V curves different shapes.
Put it right: The correct curves are proportional and therefore identical in shape.
Showing discharge current in the same direction as charging current.
Put it right: The correct discharge current flows the opposite way.
Exam tips
- Sketch Q, V and I on separate axes but with the same time scale so the shared time constant is visible.
- State the initial value of each quantity before sketching, especially for current during charging.
- Use the relationship Q = CV to justify why the Q and V curves have the same shape.
Try the lesson
The start of the Capacitor charge and discharge (A-level only): Corresponding graphs for Q, V and I against time for charging and discharging. lesson, made from checked teaching notes for this specification point.
Have a go first
A capacitor is charging through a resistor from a constant voltage DC supply. Which pair of quantities both decrease exponentially with time?
Listen
For a charging capacitor, Q and V both rise from zero towards maximum values, while I starts at its largest value and decays towards zero. The Q and V curves have the same shape because Q = CV, so they are proportional. The current curve is also exponential but starts high, because at the first instant the capacitor has no p.d. and the supply p.d. is across the resistor. On discharge, Q, V and I all fall exponentially from their initial values towards zero, and I is in the opposite direction to the charging current. A reliable method is to write the initial value and the asymptote for each quantity, then sketch all three curves on the same time axis so their relationships are clear. A strong answer earns marks for these points. During charging, Q and V rise from zero and approach maximum values asymptotically. During charging, I starts at a maximum and decays towards zero. During discharging, Q, V and I all decay from their initial values towards zero. The Q and V graphs are proportional because Q = CV, so they have the same shape and the same time constant. Exam tip: Sketch Q, V and I on separate axes but with the same time scale so the shared time constant is visible.
Key words
Say what each word means before you turn the card.
Proportionality of charge and p.d.
Try answering aloud or in your head before turning the card.
Exponential decay
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Current direction in capacitor circuits
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Time constant
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See every definition
- Proportionality of charge and p.d.
- The Q and V curves have the same shape because Q = CV, so they are proportional.
- Exponential decay
- On discharge, Q, V and I all fall exponentially from their initial values towards zero.
- Current direction in capacitor circuits
- The discharging current direction is opposite to the charging current direction.
- Time constant
- All three quantities share the same time constant τ = RC, so their graphs change at the same rate.
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