Copyright 20 13 Dorling Kindersley (India) Pvt. Ltd

Y
eq
 
=
Y
1
+ 
Y
2
+ 
...
+ 
Y
n
The nodal analysis and mesh analysis techniques developed for memoryless circuits apply 
to phasor equivalent circuits with no change except that 
impedance 
Z
takes the place 
of 
resistance R
and 
admittance 
Y
 
takes the place of 
conductance G
. Nodal Conductance 
Matrix will get called Nodal Admittance Matrix 
Y
m
and Mesh Resistance Matrix will get 
called Mesh Impedance Matrix 
Z
m
in the sinusoidal steady-state analysis using phasor 
equivalent circuits. They will be symmetric complex matrices if the phasor equivalent 
circuit contains no dependent sources. 
7.6.2 
nodal analysis and mesh analysis of phasor equivalent circuits – examples
The nodal analysis and mesh analysis techniques for obtaining sinusoidal steady-state response 
quantities using phasor equivalent circuit is illustrated through some examples in this sub-section.
example: 7.6-1
Find the steady-state current and average power dissipated in the resistor in an R
-
L series circuit with 
R 
=
100 
Ω
and L 
=
1 H when driven by a switched sinusoidal source v
S
(t) 
=
325 sin100
p
t u(t) V.
Solution
That v
S
(t) 
=
325 sin100
p
t u(t) V makes it clear that the sinusoidal source was switched on to the circuit 
only at t 
=
0. Hence, the steady-state situation will come up in the circuit only after some time and we 
should not expect the solution that we work out based on phasor equivalent circuit to hold during the 
initial period after switching on the source.
The angular frequency of the source is 
w
=
100
p
rad/sec. The value of reactance of the 1H inductor 
at this angular frequency 
=
100
p
×
1 
=
314.15 
Ω
and hence the impedance of this inductor is j314.15 
Ω
. 
Note that reactance is a real number, whereas impedance is a complex number.
We need to represent the source function in cosine form first. v
S
(t) 
=
325 sin100
p
t 
=
325 cos (100
p
t 
– 90
°
). Therefore, the phasor representation of the source is