PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Alternating Current Analysis 235

or

vt()
ImLR^22 Xcos(t)

where θ = tan−^1 (XL/R)

Note that |Z| = (^) √

---

R^2 + XL^2 (in ohms) represents the total impedance magnitude of
the RL series circuit.
R.3.32 The behavior of the impedances of inductors and capacitors can be expressed in
phasor form as
XjLLL()| |



∠





2 

XjCCC()/ |/( )|



 11

2

∠







The relation between the current and voltage for each of the three elements R, L,

and C is expressed in terms of the phasor diagrams shown* in Figure 3.2.

R.3.33 The inverse of the impedance Z (G = 1/Z) is called the admittance G, with units

1/Ω = Ω−^1 also referred to by the unit Siemen (sie).

R.3.34 For example, assume that the three elements R, L, and C are connected in series.

Compute the equivalent impedance Z and admittance G for the following case:

R = 10 
, L = 0.02 H, C = 20 F, a n d  = 1000 rad/s

*^ Complex quantities are usually expressed in electrical engineering in polar form rather than in exponential

form. The abbreviated complex representation is the phasor.

FIGURE 3.2

Phasor diagrams of R, L, and C.

R

+

vL

• 
  

i(t) iC(t)

LC

+

vR

• 
  

+

vC

• 
  

iL(t)

iR vR

vL

iL

iC

vC