Question

A resistance of 20 Ω, an inductance of 0.2 H and a capacitance of 100 μF are connected in series across 220-V, 50-Hz mains. Determine the following (a) impedance (b) current (c) voltage across R, L and C (d) power in watts and VA (e) p.f. and angle of lag

Answer 1

X_C = 0.2 × 314 = 63Ω , C = 10μF = 100 × 10⁻⁶ = 10⁻⁴ farad

X_C = 1/ωC = 1/(314 x 10^-4) = 32Ω, X = 63 − 32 = 31 Ω (inductive)

(a) Z = √(20² + 31)² = 37 Ω 

(b) I = 220/37 = 6 A (approx)

(c) V_R = I × R = 6 × 20 = 120 V; V_L = 6 × 63 = 278 V, 

V_C = 6 × 32 = 192 V 

(d) Power in V_A = 6 × 220 = 1320 

Power in watts = 6 × 220 × 0.54 = 713 W 

(e) p.f. = cos φ = R/Z = 20/37 = 0.54; φ = cos⁻¹(0.54) = 57°18′