Page 343 - Basic Electrical Engineering

Multiplication

V = V × V = V ∠θ × V ∠θ in the polar form
2
1
1
1
1
2
1
= V V ∠(θ + θ ), angles are added algebraically
2
1
2
1
Division

angles are subtracted algebraically

Example 3.12 A coil having a resistance of 5 Ω and inductance of 30 mH
in series are connected across a 230 V, 50 Hz supply. Calculate current,

power factor, and power consumed.

Solution:

R = 5 Ω

−3
L = 30 ×10 H
Inductive reactance, X = ωL = 2πfL
L
−3
X = 2 × 3.14 × 50 × 30 × 10 Ω
L
= 9.42 Ω

Impedance, Z = R + jX = 5 + j9.42
L

−1
= 10.66 ∠tan 1.884