AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
LC resonance filters (A-level only): Capacitance as spring analogy.
In an LC circuit, the capacitor stores energy in its electric field and provides the restoring effect that drives oscillations, just as a spring stores elastic potential energy and provides the…
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 3 of 4
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
In an LC circuit, the capacitor stores energy in its electric field and provides the restoring effect that drives oscillations, just as a spring stores elastic potential energy and provides the restoring force. The energy stored, ½CV² or ½Q²/C, is analogous to ½kx². A larger capacitance C means more charge is stored for a given potential difference, so the oscillation is slower, mirroring how a softer spring (smaller k) gives a longer period. Together with the inductance-as-mass analogy, this explains why the angular frequency is ω = 1/√(LC). When analysing the circuit, treat charge as displacement and current as velocity, so the capacitor's voltage corresponds to the spring's restoring force.
What earns the marks
- States that a capacitor stores energy in its electric field, analogous to a spring storing elastic potential energy.
- Links the energy expressions ½Q²/C or ½CV² to ½kx².
- Explains that a larger capacitance gives slower oscillations for a given inductance, as a softer spring gives a longer period.
- Uses the analogy to justify ω = 1/√(LC) for free oscillations in an ideal LC circuit.
- Identifies charge as the analogue of displacement and current as the analogue of velocity.
Common mistakes and how to put them right
Confusing capacitance with resistance.
Put it right: Capacitance stores energy, whereas resistance dissipates it.
Thinking the spring analogy means the capacitor physically stretches.
Put it right: It is a conceptual correspondence between restoring mechanisms.
Assuming a larger C always increases frequency.
Put it right: Increasing C decreases ω because ω = 1/√(LC).
Exam tips
- Use the energy expressions to show the parallel between ½Q²/C and ½kx².
- Explain how changing C affects the resonant frequency of an LC circuit.
- State that the analogy is between electrical and mechanical oscillators, not a literal equivalence.
Try the lesson
The start of the LC resonance filters (A-level only): Capacitance as spring analogy. lesson, made from checked teaching notes for this specification point.
Have a go first
In the mass-spring analogy for an LC circuit, the potential energy stored in the spring (1/2 kx^2) is analogous to the energy stored in the capacitor. If displacement x is analogous to charge Q, which electrical quantity is analogous to the spring constant k?
Listen
In an LC circuit, the capacitor stores energy in its electric field and provides the restoring effect that drives oscillations, just as a spring stores elastic potential energy and provides the restoring force. The energy stored, ½CV² or ½Q²/C, is analogous to ½kx². A larger capacitance C means more charge is stored for a given potential difference, so the oscillation is slower, mirroring how a softer spring (smaller k) gives a longer period. Together with the inductance-as-mass analogy, this explains why the angular frequency is ω = 1/√(LC). When analysing the circuit, treat charge as displacement and current as velocity, so the capacitor's voltage corresponds to the spring's restoring force. A strong answer earns marks for these points. States that a capacitor stores energy in its electric field, analogous to a spring storing elastic potential energy. Links the energy expressions ½Q²/C or ½CV² to ½kx². Explains that a larger capacitance gives slower oscillations for a given inductance, as a softer spring gives a longer period. Uses the analogy to justify ω = 1/√(LC) for free oscillations in an ideal LC circuit. A common slip: Confusing capacitance with resistance. Instead, capacitance stores energy, whereas resistance dissipates it. Exam tip: Use the energy expressions to show the parallel between ½Q²/C and ½kx².
See it
Key words
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Energy storage in electric fields
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Restoring force and simple harmonic motion
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Resonance in LC circuits
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Analogy between electrical and mechanical systems
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See every definition
- Energy storage in electric fields
- A capacitor stores energy in its electric field, analogous to a spring storing elastic potential energy.
- Restoring force and simple harmonic motion
- The capacitor provides the restoring effect that drives oscillations, just as a spring provides the restoring force.
- Resonance in LC circuits
- A larger capacitance gives slower oscillations for a given inductance, as a softer spring gives a longer period, with angular frequency ω = 1/√(LC).
- Analogy between electrical and mechanical systems
- Charge is treated as displacement and current as velocity, so the capacitor's voltage corresponds to the spring's restoring force.
Label the diagram
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