Introduction to Electric Circuits

Example 4.10

4.4 Complex notation 85

Represent the following currents on an Argand diagram: (1)/1 = (2 + j3) A
(2) I2=(-5+j2) A (3) 13=(4-j4) A (4)I4=(-4-j5)A
(5) 15 = 5/100 ~ A (6) 16 = 3/--10 ~ A.

Solution

1 I1 has 2 units along the positive real axis and 3 units along the positive

imaginary axis. Its length is u + 32) = 3.61 A.

2 12 has 5 units along the negative real axis and 2 units along the positive
imaginary axis. Its magnitude is V/(52 + 22) -- 5.39 A.
3 13 has 4 units along the positive real axis and 4 units along the negative
imaginary axis. Its magnitude is ~r + 42) -- 5.66 A.
4 14 has 4 units along the negative real axis and 5 units along the negative
imaginary axis. Its magnitude is V/(42 + 52) - 6.4 A.
5 15 has a magnitude of 5 A and is at 100 ~ in an anticlockwise (positive)
direction from the reference (i.e. the positive real axis).
6 16 has a magnitude of 3 A and is placed 10 ~ in a clockwise (negative)
direction from the positive real axis.
These are shown on the Argand diagram in Fig. 4.23.
I51~ I +j
I I-- I
I1
I2 /t 3 /4

~+

13

14 5

-j

Figure 4.23

Rectangular and polar coordinates

The phasor diagram of Fig. 4.24 shows a phasor V and its two components in

Figure 4.24

jb = V sin

/ / r- "-- r (reference)

a = V cos