AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
LC resonance filters (A-level only): Inductance as mass analogy.
In an LC circuit, the inductor opposes changes in current, just as mass opposes changes in velocity.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 2 of 4
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
In an LC circuit, the inductor opposes changes in current, just as mass opposes changes in velocity. Energy stored in the magnetic field of an inductor, ½LI², plays the role of kinetic energy, ½mv². A larger inductance L means a slower build-up or decay of current for a given potential difference, mirroring how a larger mass accelerates less under the same force. This analogy helps explain why the angular frequency of free oscillations is ω = 1/√(LC): the inductor behaves like the inertial mass and the capacitor like the spring. When analysing a circuit, treat current as the analogue of velocity and charge as the analogue of displacement, so the inductor's back e.m.f. corresponds to inertia.
What earns the marks
- States that an inductor opposes change of current, analogous to mass opposing change of velocity.
- Links magnetic field energy ½LI² to kinetic energy ½mv².
- Explains that larger L gives slower current change for a given p.d., as larger mass gives smaller acceleration for a given force.
- Uses the analogy to justify ω = 1/√(LC) for free oscillations in an ideal LC circuit.
- Identifies current as the analogue of velocity and charge as the analogue of displacement.
Common mistakes and how to put them right
Treating inductance as a source of energy rather than a store.
Put it right: The magnetic field stores energy and returns it to the circuit.
Confusing the mass analogy with resistance.
Put it right: Resistance dissipates energy, whereas mass and inductance store it.
Assuming the analogy means the inductor has literal mass.
Put it right: It is a mathematical and conceptual correspondence only.
Exam tips
- Use the analogy to explain why increasing L lowers the resonant frequency.
- When deriving ω, compare the energy expressions ½LI² and ½mv² to show the parallel.
- State clearly that the analogy is between electrical and mechanical oscillators, not a physical identity.
Try the lesson
The start of the LC resonance filters (A-level only): Inductance as mass analogy. lesson, made from checked teaching notes for this specification point.
Have a go first
In the mass–spring analogy for an LC circuit, which electrical quantity plays the role of the mass?
Listen
In an LC circuit, the inductor opposes changes in current, just as mass opposes changes in velocity. Energy stored in the magnetic field of an inductor, ½LI², plays the role of kinetic energy, ½mv². A larger inductance L means a slower build-up or decay of current for a given potential difference, mirroring how a larger mass accelerates less under the same force. This analogy helps explain why the angular frequency of free oscillations is ω = 1/√(LC): the inductor behaves like the inertial mass and the capacitor like the spring. When analysing a circuit, treat current as the analogue of velocity and charge as the analogue of displacement, so the inductor's back e.m.f. corresponds to inertia. A strong answer earns marks for these points. States that an inductor opposes change of current, analogous to mass opposing change of velocity. Links magnetic field energy ½LI² to kinetic energy ½mv². Explains that larger L gives slower current change for a given p.d., as larger mass gives smaller acceleration for a given force. Uses the analogy to justify ω = 1/√(LC) for free oscillations in an ideal LC circuit. A common slip: Treating inductance as a source of energy rather than a store. Instead, the magnetic field stores energy and returns it to the circuit. Exam tip: Use the analogy to explain why increasing L lowers the resonant frequency.
See it
Key words
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Energy storage in magnetic fields
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Inertia and opposition to change
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Simple harmonic motion analogy
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Resonance in LC circuits
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See every definition
- Energy storage in magnetic fields
- The magnetic field of an inductor stores energy as ½LI², which plays the role of kinetic energy ½mv².
- Inertia and opposition to change
- An inductor opposes changes in current, just as mass opposes changes in velocity, and its back e.m.f. corresponds to inertia.
- Simple harmonic motion analogy
- The inductor behaves like the inertial mass and the capacitor like the spring, with current the analogue of velocity and charge the analogue of displacement.
- Resonance in LC circuits
- The angular frequency of free oscillations is ω = 1/√(LC), justified by treating the inductor as inertial mass and the capacitor as the spring.
Label the diagram
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