LC resonance filters (A-level only): Energy (voltage) response curve.

The idea

An energy or voltage response curve shows how the output of an LC filter varies with driving frequency. In a series LC circuit, current peaks at the resonant frequency f₀, while the voltage across the capacitor or inductor peaks at frequencies slightly away from f₀. In a parallel LC circuit, the impedance is maximum at resonance, so the voltage across the parallel combination peaks at f₀. The curve is often plotted as output voltage against frequency, with a sharp maximum or minimum at f₀. The width of the peak relates to the quality factor Q: a higher Q gives a narrower, sharper resonance. You should be able to sketch the general shape, label the resonant frequency, and explain how the curve changes when L, C or resistance changes.

What earns the marks

• Sketch a graph with frequency on the horizontal axis and output voltage or energy on the vertical axis.
• Identify the resonant frequency f₀ as the frequency at which the response is maximum or minimum, depending on circuit type.
• Describe the shape of the curve: a sharp peak for a high-Q circuit and a broader peak for a low-Q circuit.
• Explain that at resonance the reactances cancel, so impedance is minimum in a series circuit and maximum in a parallel circuit.
• Relate the peak width to energy loss and damping, noting that increased resistance broadens the response.
• Use the curve to determine the resonant frequency or to compare the selectivity of two filter designs.

Common mistakes and how to put them right

• Drawing a curve that peaks at zero frequency instead of at the resonant frequency.

  Put it right by marking f₀ clearly on the frequency axis.

• Confusing the current response with the voltage response.

  Put it right by checking whether the question asks about current or voltage across a specific component.

• Assuming the curve is symmetrical for all circuits.

  Put it right by noting that practical resonance curves can be asymmetric when resistance is significant.

• Ignoring the effect of resistance on peak height and width.

  Put it right by stating that greater resistance reduces the peak and broadens the curve.

Exam tips

• Label both axes with quantity and unit, and mark f₀ on the frequency axis.
• Use a ruler to draw smooth curves and make the peak or trough clearly visible.
• When comparing two curves, state which has the higher Q and justify it by referring to peak width.
• If asked to explain the curve, link the shape to the frequency-dependent reactances X_L and X_C.