240 Practical MATLAB® Applications for Engineers
Indicate also the type and its equivalent circuit in term of its simplest element
representation.
ANALYTICAL Solution
The phasor diagram in which I and V are indicated is shown in Figure 3.11.
The equivalent impedance can be calculated as indicated as follows:
Z V
I
545
230
5
2
45 30 2 5 75
∠
∠−
∠().∠ (using peak values)
its trigonometric form is Z = 2.5 cos(75°) + j2.5 sin(75°) Ω.
That means that the equivalent impedance is an RL circuit, with R = 2.5 cos(75°) Ω and
L =
25 sin(75°)
__________
120 π
H.
R.3.43 Let us evaluate now the voltage v(t) of a series RLC circuit, if the current i(t) is given
by i(t) = Im cos(ωt).
ANALYTICAL Solution
ZRjL
C
1
and
ZR L
C
^2
1 2
The voltage across the series RLC is then given by
v(t) = Im|Z|c o s (t + )
= 45°
Imaginary axis
Real axis
= 30°
V = 5
I = 2
FIGURE 3.11
Phasor diagram of R.3.42.