Series LCR Circuit question from NEET 2023

Answer: (a)

1. Circuit (a) has a d.c. source: the inductor has no reactance in steady d.c., so $Z_1 = R = 10\ \Omega$.
2. Circuit (b): $X_C = \frac{1}{2\pi f C} = \frac{1}{2\pi \times 50 \times \frac{10^3}{\pi} \times 10^{-6}} = 10\ \Omega$
3. $Z_2 = \sqrt{10^2 + 10^2} = 10\sqrt{2}\ \Omega$
4. So $Z_1 < Z_2$: answer (a).