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Charging and discharging questions
Put a resistor in the path and a capacitor charges and discharges along curves rather than straight lines. Charge, potential difference and current carry the topic. On discharge all three fall together along the same shape; on charging the current does the opposite, starting large and falling to zero as the other two rise.
18 original questions · 46 marks · the charging and discharging notes · Capacitance
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Describe the shape of the charge-time graph for a capacitor discharging through a resistor.
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Exponential decay from the initial (maximum) charge (1); the charge falls quickly at first, then ever more slowly, approaching zero without reaching it (1).Describe how the current changes with time while a capacitor charges through a resistor.
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The current is a maximum at the instant charging begins (1); it then decreases exponentially towards zero as the capacitor charges (1).State how the current in a capacitor circuit can be found from the charge-time graph.
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The current is the magnitude of the gradient of the charge-time graph, I = ΔQ/Δt; on discharge that gradient is negative because charge is leaving the plates (1).State what is represented by the area under a current-time graph for a capacitor discharging through a resistor.
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The total charge transferred (the charge that leaves the capacitor) (1).A capacitor is charged through a resistor from a 5.0 V supply. When charging is complete, state the potential difference across the capacitor and the potential difference across the resistor.
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The capacitor pd equals the supply pd, 5.0 V (1); the resistor pd is zero, because the current has fallen to zero (1).An initially uncharged capacitor is charged through a resistor. Describe how the potential difference across the resistor varies with time.
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It starts at its maximum value, equal to the full supply pd (1); it then decreases (exponentially) towards zero as the capacitor pd rises towards the supply pd (1).A capacitor charged to 12 V is discharged through a 1.0 kΩ resistor. Calculate the initial discharge current.
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I0 = V/R = 12/1000 (1)
I0 = 0.012 A (12 mA) (1)A capacitor is charged from a 6.0 V supply through a 2.0 kΩ resistor. State the value of the charging current at the start of charging and when the capacitor is fully charged.
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Initial current I0 = V/R = 6.0/2000 = 0.0030 A (3.0 mA) (1)
Final current = 0 when fully charged (1).A capacitor is charged through a fixed resistor. Describe and explain the shapes of the graphs of potential difference across the capacitor against time and of current against time.
A 100 μF capacitor is fully charged to 9.0 V. Calculate the charge stored and the energy stored.
A student discharges a capacitor through a resistor and uses a datalogger to record the charge-time graph. The tangent to the graph at t = 0 has a gradient of −4.0 × 10−4 C s−1. The initial potential difference across the capacitor is 6.0 V. Determine the resistance of the resistor.
An initially uncharged capacitor is fully charged from a 9.0 V supply through a resistor. The area under the current-time graph for the whole charging process is 5.4 mC. Determine the capacitance of the capacitor.
A 12 V supply charges a capacitor through a 15 kΩ resistor. At one instant the potential difference across the capacitor is 7.5 V. Calculate the potential difference across the resistor and the charging current at this instant.
A 470 μF capacitor charged to 10 V is discharged through a 2.2 kΩ resistor. Calculate the initial charge stored and the initial discharge current.
A 1000 μF capacitor is charged to 12 V and then fully discharged through a resistor. Determine the total energy dissipated in the resistor.
Explain why the current decreases with time as a capacitor discharges through a resistor.
A 2200 μF capacitor in an emergency door alarm is charged to 6.0 V. The sounder stops working when the pd across the capacitor has fallen to 3.0 V. Calculate the energy transferred to the sounder circuit between these two pds.
A student is building a circuit in which a 4700 μF capacitor charges from a 12 V supply through a single resistor. Two resistors are available: 100 Ω and 100 kΩ. The student wants the capacitor to charge as quickly as possible, but the charging current must never exceed 50 mA. Deduce which resistor the student should use.
The same practice on paper: the printable workbook for this topic, questions and a worked answer book.
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