Question

(i) Derive the impedance of an R-C series circuit connected to an AC source v = v_m sin(ωt).
(ii) When does an inductor act as a conductor? Explain.
(iii) A lamp (R) and inductor (L) in series with 220V-50Hz AC give 11A. With 110V DC, it gives 11A. Find L.

Hint:

Impedance, Inductive Reactance, AC circuits

Answer 1

(i) Impedance Z = sqrt(R² + X_c²), where X_c = 1/ωC. (ii) Inductor acts as a conductor in DC because X_L = 2πfL = 0 when f = 0. (iii) R = V_dc/I = 10Ω. Z = V_ac/I = 20Ω. Z = sqrt(R² + X_L²). X_L = sqrt(Z² - R²) = 10√3 Ω. L = X_L/ω = X_L/(2πf) ≈ 55 mH.