PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

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.