A circuit connected to an ac source of emf e = e_0 sin (100 t) with t in seconds, gives a phase difference of π/4 between the emf e and current i. Which of the following circuits will exhibit this?

Correct option is D. RC circuit with R = 1 kΩ and C = 10 mF
Given phase difference = π/4
and ω = 100 rad/s
⇒ Reactance (X) = Resistance (R)
now by checking options
option (1)
R = 1000 Ω and X_C = 1/(10⁻⁶ × 100) = 10⁴ Ω
Option (2)
R = 10³ Ω and X_L = 10⁻³ × 100 = 10⁻¹ Ω
option (3)
R = 10³ Ω and X_L = 10 × 10⁻³ × 100 = 1 Ω
Option (4)
R = 10³ Ω and X_C = 1/(10 × 10⁻⁶ × 100) = 10³ Ω
Clear option (4) matches the given condition