Question

In a circuit, the applied voltage is found to lag the current by 30°. 

(a) Is the power factor lagging or leading ? 

(b) What is the value of the power factor ? 

(c) Is the circuit inductive or capacitive? 

In the diagram of Fig , the voltage drop across Z₁ is (10 + j0) volts. Find out

 

(i) the current in the circuit (ii) the voltage drops across Z₂ and Z₃ (iii) the voltage of the generator

Answer 1

(a) Power factor is leading because current leads the voltage. 

(b) p.f. = cos 30° = 0.86 (lead) 

(c) The circuit is capacitive. 

(i) Circuit current can be found by dividing voltage drop V₁ by Z₁

I = (10 + j0)/(3 + j4) 

= (10∠ 0°)/(5 ∠ 53.1°) = 2 ∠ - 53.1º 

= 2(cos53.1º - jsin53.1º)

= 2 (0.6 −j 0.8) = 1.2 −j 1.6

Z₂ = 2 + j 3.46; V₂ = IZ₂ 

= (1.2 −j 1.6) (2 + j3.46) = (7.936 + j 0.952) volt 

V₃ = (1.2 − j 1.6) (1− j 7.46) 

= (− 10.74 −j 10.55) volt

(ii) V = V₁ + V₂ + V₃ 

= (10 + j0) + (7.936 + j 0.952) + (− 10.74 −j 10.55) 

= (7.2 −j 9.6) = 12 ∠ − 53.1°

Incidentally, it shows that current I and voltage V are in phase with each other