A resistor, an inductor and a capacitor are connected in series with a variable frequency source of alternating emf. At resonance, the amplitude of current depends on :
(A) Resistance
(B) Inductance
(C) Capacitance
(D) Frequency of source
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) only
The impedance of a series LCR circuit is
\( \displaystyle Z = \sqrt{R^{2} + (X_L - X_C)^{2}} \)
At resonance \( X_L = X_C \), so the reactances cancel and \( Z = R \). The current amplitude is then
\( \displaystyle I_0 = \frac{V_0}{Z} = \frac{V_0}{R} \)
(A) Resistance — Correct. R is the only quantity left in the impedance at resonance, so it alone fixes the current amplitude for a given source voltage.
(B) Inductance — Incorrect. L decides where resonance happens, \( \omega_0 = 1/\sqrt{LC} \), but its reactance is cancelled by that of the capacitor, so it does not appear in \( I_0 \).
(C) Capacitance — Incorrect. For the same reason, C only sets the resonant frequency; it does not change the current amplitude at resonance.
(D) Frequency of source — Incorrect. At resonance the frequency is fixed at \( \omega_0 \), and \( I_0 = V_0/R \) contains no frequency term.
NCERT (2026-27):
Resonance – “… So if ω is varied, then at a particular frequency ω0, Xc = XL, and the impedance is minimum
\( \displaystyle \left(Z = \sqrt{R^2 + 0^2} = R\right) \)
This frequency is called the resonant frequency: … At resonant frequency, the current amplitude is maximum; im = vm/R.”