Given below are two statements :
Statement I : In an LCR series circuit, current is maximum at resonance.
Statement II : Current in a purely resistive circuit can never be less than that in a series LCR circuit when connected to same voltage source.
In the light of the above statements, choose the correct from the options given below :

Solution

Physics sir · 4 steps

Write the impedance Z = √(R² + (X_L - X_C)²), and both statements follow from it at once.

1. Current from impedance. In a series LCR circuit the current amplitude is I = V/Z. The smaller the impedance, the larger the current.

   Z = √(R² + (X_L - X_C)²) ≥ R

2. Statement I. At resonance X_L = X_C, so the bracket is zero and Z takes its smallest value, Z = R. Smallest Z means largest current, so Statement I is true.
3. Statement II. A purely resistive circuit has Z = R, so its current is V/R. The LCR circuit always has Z ≥ R, so its current V/Z is at most V/R. The resistive current can equal it at resonance but never be less, so Statement II is true.
4. So. Both statements are true, which is option (c).

The idea to keep. In a series LCR circuit Z can never drop below R. Resonance only cancels the reactances, so it brings Z down to R and no further.

Answer from the NTA final answer key. Solution by PrepWiser.