MHTCET 20 Apr 2026 Shift 2 Paper

Concept:For a pure resistive circuit, impedance is just resistance. For a series LCR circuit, impedance is always greater than or equal to resistance.Explanation:For circuit (A), there is no inductor or capacitor, so its impedance is $Z_A = R = 30\ \Omega$.The r.m.s. current in circuit (A) is $I_A = \frac{V_{rms}}{Z_A} = \frac{V_{rms}}{R}$.For circuit (B), which is a series LCR circuit, impedance is given by $Z_B = \sqrt{R^2 + (X_L - X_C)^2}$.Since $(X_L - X_C)^2 \ge 0$, we get $Z_B \ge R$.Thus, $Z_B \ge Z_A$.Both circuits are connected to the same supply voltage $V_{rms}$.Current is inversely proportional to impedance, so $I_B = \frac{V_{rms}}{Z_B}$ and $I_A = \frac{V_{rms}}{Z_A}$.Because $Z_B \ge Z_A$, it follows that $I_B \le I_A$.At resonance, $X_L = X_C$, so $Z_B = R$ and therefore $I_B = I_A$.In all other cases, $Z_B > R$, giving $I_B < I_A$.Hence, the r.m.s. current in circuit (B) can never be larger than that in circuit (A).Answer:Option D: The r.m.s. current in (B) can never be larger than that in (A).