Capacitors — OCR A-Level Physics
Test yourself on Capacitors with OCR A-Level practice questions.
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Capacitors explained
A capacitor stores charge on two conductors separated by an insulator.
Read the full explanation
Its capacitance C is defined as the charge stored per unit potential difference: C = Q/V, where Q is the magnitude of charge on one plate and V is the potential difference across the capacitor. The unit of capacitance is the farad (F); one farad is one coulomb per volt, so 1 F = 1 C V⁻¹. Typical capacitors have values in microfarads (1 μF = 1 × 10⁻⁶ F), nanofarads (1 nF = 1 × 10⁻⁹ F) or picofarads (1 pF = 1 × 10⁻¹² F). Rearranged, Q = CV and V = Q/C.
(b) charging and discharging of a capacitor or capacitor plates with reference to the flow of electrons
A capacitor stores charge when a potential difference drives electrons around a circuit. During charging, electrons flow from the negative terminal of the supply onto one plate, giving it a net negative charge, while electrons leave the opposite plate towards the positive terminal, leaving it with an equal positive charge. The two plates therefore carry charges of equal magnitude and opposite sign. During discharging, the supply is removed and the plates reconnect through a component; electrons flow from the negative plate, through the external circuit, back to the positive plate until the potential difference across the capacitor falls to zero. The electron flow is opposite to conventional current in the external circuit.
(c) total capacitance of two or more capacitors in series; 1/C = 1/C₁ + 1/C₂ + ...
When capacitors are connected in series, the reciprocal of the total capacitance equals the sum of the reciprocals of the individual capacitances: 1/C = 1/C₁ + 1/C₂ + ... . This means the total capacitance is always less than the smallest individual capacitance. For example, two 10 μF capacitors in series give 1/C = 1/10 + 1/10 = 2/10, so C = 5 μF. The same charge Q is stored on each capacitor in series, and the potential differences add to the supply p.d. The formula must be rearranged to find C after summing the reciprocals.
(d) total capacitance of two or more capacitors in parallel; C = C₁ + C₂ + ...
When capacitors are connected in parallel, the total capacitance is the sum of the individual capacitances: C = C₁ + C₂ + ... . This means the total capacitance is always greater than the largest individual capacitance. For example, two 10 μF capacitors in parallel give C = 10 + 10 = 20 μF. In a parallel arrangement, each capacitor has the same potential difference across it, and the total charge stored is the sum of the charges on the individual capacitors. The formula is used directly without taking reciprocals.
(e)
This row is a guided reading entry for section 6.1.1 Capacitors. The statement is incomplete, so the learner should use the official OCR A Level Physics A specification to identify the full learning outcome (e) and read the surrounding context. The learner should locate the specification document, find section 6.1.1, and read outcome (e) in full. They should note any formula, definition or application it contains, and check how it connects to outcomes (b), (c) and (d) on charging, discharging, series and parallel capacitance. The learner should then summarise the outcome in their own words and identify any practical work or mathematical skills it requires.
(i) analysis of circuits containing capacitors, including resistors
Circuits containing both capacitors and resistors can be analysed using Kirchhoff's laws and the relationship \(Q = CV\). In a direct current (d.c.) circuit, a capacitor initially uncharged acts momentarily like a short circuit, so the initial current is determined entirely by the resistors (\(I = V/R\)). As charge accumulates on the capacitor plates, its potential difference increases, which reduces the current. Once fully charged, the capacitor's p.d. equals the supply voltage (in a simple series circuit), and it acts as an open circuit, blocking any steady d.c. current. Analysis involves calculating initial currents, final charges, and steady-state potential differences across components using series and parallel rules, without requiring the exponential time-dependent equations covered later in the specification.
(ii) techniques and procedures used to investigate capacitors in both series and parallel combinations using ammeters and voltmeters.
Investigating capacitors in series and parallel uses ammeters in series to measure current and voltmeters in parallel to measure p.d. across each component. For series capacitors, the reciprocal rule 1/C_total = 1/C₁ + 1/C₂ gives a smaller total capacitance; for parallel, C_total = C₁ + C₂ gives a larger total. A practical procedure charges the combination and records current and p.d. at intervals. Because charging current varies, charge Q is found from the area under an I-t graph, not simply Q = It, unless a constant current circuit is used. Correct meter placement matters: an ammeter must be in series with the branch, a voltmeter in parallel. Readings verify the combination rules.
Your focus
- Define capacitance using C = Q/V and state the unit farad.
- Rearrange C = Q/V to find charge or potential difference in calculations.
- Convert between farads and prefixed units such as μF, nF and pF.
Show all 21 objectives
- Describe the charging of a capacitor in terms of electron flow from and to the supply.
- Describe the discharging of a capacitor in terms of electron flow through the external circuit.
- State that the charges on the two plates are equal in magnitude and opposite in sign.
- State and use the formula 1/C = 1/C₁ + 1/C₂ + ... for capacitors in series.
- Calculate the total capacitance of two or more capacitors connected in series.
- Explain why the total capacitance in series is less than the smallest individual capacitance.
- State and use the formula C = C₁ + C₂ + ... for capacitors in parallel.
- Calculate the total capacitance of two or more capacitors connected in parallel.
- Explain why the total capacitance in parallel is greater than the largest individual capacitance.
- Locate and read outcome (e) in section 6.1.1 of the OCR A Level Physics A specification.
- Summarise the full content of outcome (e) in your own words.
- Relate outcome (e) to the charging, discharging, series and parallel capacitance outcomes in the same section.
- Apply \(Q = CV\) and Kirchhoff's laws to determine initial and final states of circuits containing capacitors and resistors.
- Calculate the initial current in a resistor-capacitor circuit using the supply voltage and resistance.
- Determine the final charge and potential difference of a capacitor once steady-state d.c. conditions are reached.
- Describe how to connect ammeters and voltmeters correctly when investigating capacitors.
- Apply the series and parallel rules to calculate total capacitance.
- Use the area under a current-time graph to determine charge stored and compare with predictions.
Capacitors exam tips
Marking Points
- Defines capacitance as charge stored per unit potential difference: C = Q/V.
- States that the unit of capacitance is the farad, where 1 F = 1 C V⁻¹.
- Uses the rearrangements Q = CV and V = Q/C correctly in calculations.
- Converts between farads and submultiples such as μF, nF and pF using powers of ten.
- Charging involves electron flow from the supply onto one plate and away from the other plate.
- One plate becomes negatively charged and the other becomes positively charged by an equal magnitude.
- The charge on the plates is equal in magnitude but opposite in sign.
- During discharging, electrons flow through the external circuit from the negative plate to the positive plate.
- The flow of electrons constitutes a current in the external circuit, opposite in direction to conventional current.
- Discharging continues until the potential difference across the capacitor is zero.
- The formula for capacitors in series is 1/C = 1/C₁ + 1/C₂ + ... .
- The total capacitance in series is less than the smallest individual capacitance.
- Each capacitor in series stores the same magnitude of charge.
- The potential differences across capacitors in series add to give the total potential difference.
- To find C, calculate the sum of reciprocals and then take the reciprocal of that sum.
- The formula for capacitors in parallel is C = C₁ + C₂ + ... .
- The total capacitance in parallel is greater than the largest individual capacitance.
- Each capacitor in parallel has the same potential difference across it.
- The total charge stored is the sum of the charges on the individual capacitors.
- The formula is applied by direct addition of the capacitance values.
- Apply \(Q = CV\) to calculate charge, capacitance, or potential difference in circuits with resistors.
- Use Kirchhoff's laws to determine the initial current in a circuit when an uncharged capacitor behaves momentarily as a short circuit.
- Recognise that a fully charged capacitor in a d.c. circuit acts as an open circuit, meaning no steady current flows through that branch.
- Calculate the steady-state potential difference across a capacitor by analysing the voltage drops across resistors in the rest of the circuit.
- Place an ammeter in series with the circuit branch and a voltmeter in parallel with the component being measured.
- Use the series rule 1/C_total = 1/C₁ + 1/C₂ and the parallel rule C_total = C₁ + C₂ for capacitor combinations.
- Record current and p.d. readings over time to determine charge Q from the area under an I-t graph, or use a constant current circuit.
- Compare measured total capacitance with the value predicted by the series or parallel rule.
Examiner Tips
- 💡Write the defining equation C = Q/V before substituting values so the quantities are clear.
- 💡Convert all capacitance values to farads before calculating, then convert the answer back if needed.
- 💡Check units: charge in coulombs, potential difference in volts and capacitance in farads.
- 💡State clearly that it is electrons that move, not positive charge carriers.
- 💡Use the phrase 'equal in magnitude and opposite in sign' when describing the charges on the two plates.
- 💡When describing discharging, refer to the external circuit and the direction of electron flow from the negative plate to the positive plate.
- 💡Link the end of discharging to the potential difference across the capacitor becoming zero.
- 💡Write down the formula 1/C = 1/C₁ + 1/C₂ + ... before substituting values.
- 💡After summing reciprocals, remember to invert the result to find C.
- 💡Check that your answer is smaller than the smallest individual capacitance as a quick sanity check.
- 💡Keep units consistent, for example all capacitances in μF or all in F.
- 💡Write down the formula C = C₁ + C₂ + ... before substituting values.
- 💡Check that your answer is larger than the largest individual capacitance as a quick sanity check.
- 💡Keep units consistent, for example all capacitances in μF or all in F.
- 💡Remember that in parallel the potential difference across each capacitor is the same.
- 💡Open the official OCR A Level Physics A specification and navigate to section 6.1.1 Capacitors.
- 💡Read outcome (e) in full and write a short summary in your own words.
- 💡Link outcome (e) to the charging, discharging, series and parallel content already covered in this section.
- 💡Note any formula, unit or practical skill mentioned in outcome (e) and check you can use it.
- 💡For initial conditions (\(t=0\)), treat uncharged capacitors as having zero p.d., meaning they act like a plain wire.
- 💡For steady-state conditions (fully charged), treat capacitors as breaks in the circuit and calculate the p.d. across them based on the remaining active circuit.
- 💡Always check whether the question asks for the initial current or the final steady-state charge.
- 💡Draw the circuit diagram clearly, showing ammeter in series and voltmeter in parallel before describing readings.
- 💡State the combination rule you are testing and show the substitution of measured values.
- 💡Explain how to find charge from the area under a current-time graph when describing the procedure.
Common Mistakes
- Using the total charge on both plates in C = Q/V; Q is the magnitude of charge on one plate.
- Treating the farad as a base unit; it is defined as one coulomb per volt.
- Mixing up microfarads and nanofarads, for example writing 1 μF = 1 × 10⁻⁹ F instead of 1 × 10⁻⁶ F.
- Substituting the potential difference across the whole circuit for the potential difference across the capacitor.
- Thinking that positive charge physically moves onto a plate during charging; in fact electrons move, and the positive charge on one plate arises because electrons have left it.
- Believing that the two plates carry the same sign of charge; they carry equal magnitudes of opposite sign.
- Assuming that electrons flow through the dielectric between the plates; in a capacitor, charge is stored on the plates and the external circuit carries the electron flow.
- Confusing the direction of electron flow with conventional current; electrons flow from negative to positive, opposite to conventional current.
- Adding capacitances directly for series, as if they were resistors in parallel; the correct relationship uses reciprocals.
- Forgetting to take the reciprocal of the sum to obtain C; the formula gives 1/C, not C.
- Assuming the total capacitance is greater than the largest individual capacitance; in series it is always less than the smallest.
- Mixing up the series and parallel formulas; series uses reciprocals, parallel uses direct addition.
- Using reciprocals for parallel capacitors, as if they were in series; parallel uses direct addition.
- Assuming the total capacitance is less than the largest individual capacitance; in parallel it is always greater.
- Forgetting that the potential difference is the same across each parallel branch.
- Adding charges instead of capacitances when the question asks for total capacitance.
- Assuming the incomplete statement (e) can be ignored; the learner should find the full outcome in the specification.
- Treating guided reading as a test of memory rather than a task to locate and understand the specification content.
- Reading only the single line (e) without the surrounding section context, which may link to earlier or later outcomes.
- Failing to note any formula or definition in outcome (e) and how it relates to capacitance calculations.
- Assuming a steady current flows through a capacitor in a d.c. circuit; correction: once fully charged, the capacitor blocks direct current.
- Applying exponential decay equations to find initial or final states; correction: use simple Ohm's law and Kirchhoff's laws for \(t=0\) and \(t \to \infty\) states.
- Forgetting that the p.d. across a capacitor in parallel with a resistor is equal to the p.d. across that resistor.
- Connecting the ammeter in parallel with a component; an ammeter must be in series to measure current.
- Connecting the voltmeter in series; a voltmeter must be in parallel with the component whose p.d. is measured.
- Using Q = It for a varying current; charge must be found from the area under the I-t graph unless current is kept constant.