Question

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 the same voltage source. 
In the light of the above statements, choose the correct from the options given below.

• A. Statement I is true but Statement II is false
• B. Statement I is false but Statement II is true
• C. Both Statement I and Statement II are true
• D. Both Statement I and Statement II are false

Answer 1

The Correct Option is C

Statement-I: \[ I_m = \frac{V_m}{\sqrt{R^2 + (X_L - X_C)^2}} \] When \(X_L = X_C\) (resonance condition): \[ I_m = \frac{V_m}{R} \]

At resonance, the impedance is at its minimum, resulting in the maximum current.

Statement-II: \[ I = \frac{V}{R} \] This equation applies to a purely resistive circuit.

Therefore, in a purely resistive circuit, the current is always equal to the value calculated by Ohm's law for that resistance, and cannot be less than the current in a series LCR circuit at resonance.

Both Statement I and Statement II are true.