Introduction to Electric Circuits

88 Single-phase a.c. circuits

Example 4.14

The voltages at two points A and B are given by VA = 100/-20~ and

VB- 200/_- 25 ~ V. Calculate the potential difference (VA- VB) between

them.

Solution

Subtraction is best carried out using rectangular coordinates, so converting to

this form we have

v~

v~

v~

= 100 cos 20 ~ + jl00 sin 20 ~ - (93.9 + j34.2) V

= 200 cos 25 ~ - j200 sin 25 ~ = (181 - j84.5) V

• VB = (93.9 - 181) + j(34.2 + 84.5) - (-87.1 + j118.7) V
  = 147.2/126.3~

Example 4.15

Subtract 11 = (10 + j5) A from I2

Solution

11 = (5 --j15) - (10 + j5)

= 5 -j15 - 10 -j5

= (-5 -j20) A

: (5 -j15) A.

Multiplication and division of complex quantities

These operations are best carried out using polar coordinates. For multi-
plication the magnitudes are multiplied and the angles are added; for division
the magnitudes are divided and the angles are subtracted.

Example 4.16

If A = (5 + j6) and B = (7 - jl0), obtain the product AB.

Solution

First let us use rectangular coordinates.

A•215215215215

= 35 - j50 + j42 + 60

= 95 -j8

In polar form

A • B = V'(952 + 8:)/_-tan -1 (8/95)= 95.33/_-4.8 ~