OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
(i) analysis of circuits containing capacitors, including resistors
Full specification wording
Capacitors: (i) analysis of circuits containing capacitors, including resistors
Circuits containing both capacitors and resistors can be analysed using Kirchhoff's laws and the relationship \(Q = CV\).
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 5 of 6
Study notes
From the checked teaching notes for this specification point.
The idea
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.
What earns the marks
- 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.
Common mistakes and how to put them right
Assuming a steady current flows through a capacitor in a d.c. circuit.
Put it right: Once fully charged, the capacitor blocks direct current.
Applying exponential decay equations to find initial or final states.
Put it right: 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.
Exam tips
- 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.
Try the lesson
The start of the Capacitors: (i) analysis of circuits containing capacitors, including resistors lesson, made from checked teaching notes for this specification point.
Listen
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. A strong answer earns marks for these points. 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. A common slip: Assuming a steady current flows through a capacitor in a d.c. circuit. Instead, once fully charged, the capacitor blocks direct current. Exam tip: For initial conditions (\(t=0\)), treat uncharged capacitors as having zero p.d., meaning they act like a plain wire.
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