JEE Main 2022 · 25 July · morning · Single correct · +4 / −1
To increase the resonant frequency in series LCR circuit,
- (a) source frequency should be increased.
- (b) another resistance should be added in series with the first resistance.
- (c) another capacitor should be added in series with the first capacitor.
- (d) the source frequency should be decreased.
Answer and solution
Answer (c) another capacitor should be added in series with the first capacitor.
Solution
Physics sir · 4 steps
Resonant frequency belongs to the circuit, not the source: only changing L or C can move it.
- What sets resonance. Resonance happens when X_L = X_C, that is ω L = 1/(ω C). Solving this gives a frequency fixed by L and C alone.
f₀ = 1/2π√LC
- Capacitors in series. Two capacitors in series give 1/C_(eq) = 1/C₁ + 1/C₂, so C_(eq) is smaller than either one. A smaller C makes √LC smaller and f₀ larger.
- Other options. The source frequency does not appear in f₀, so raising or lowering it changes nothing about where resonance lies. Resistance does not appear either; it only changes the height and sharpness of the resonance peak.
- So. Adding another capacitor in series lowers the net capacitance and raises the resonant frequency. The answer is (c).
The idea to keep. Resonant frequency f₀ = 1/2π√LC depends only on L and C. To raise it, reduce L or C; capacitors in series reduce C. R and the source frequency never shift it.
Answer from the NTA final answer key. Solution by PrepWiser.