Question

Draw a vector for the circuit shown in Fig.  indicating the resistance and reactance drops, the terminal voltages V₁ and V₂ and the current. Find the values of (i) the current I (ii) V₁ and V₂ and (iii) p.f

Answer 1

L = 0.05 + 0.1 = 0.15 H;

X_L = 314 × 0.5 = 47.1 Ω

X_C = 10⁶/314 × 50 = 63.7 Ω;

X = 47.1 − 63.7 = − 16.6 Ω,

R = 30 Ω,

Z = √(302 + (- 16.6)2) = 34.3Ω

(i) I = V/Z = 200/34.3 = 5.83 A, from Fig.

(ii) X_L1 = 314 × 0.05 = 15.7 Ω

Z₁ = √(10² + 15.7²) = 18.6Ω

V₁= IZ₁ = 5.83 × 18.6 

= 108.4 V 

φ₁ = cos^{− 1} (10/18.6) = 57.5° (lag) 

X_L2 = 314 × 0.1 = 31.4 Ω, X_c = − 63.7Ω, 

X = 31.4 − 63.7 = − 32.2Ω, Z₂ = √(20² + (- 32.3)²) = 221V

φ₂ = cos^{− 1} (20/38) = 58.2 (lead) 

(iii) Combined p.f. = cos φ = R/Z = 30/34.3 = 0.875 (lead), from Fig..