Solution 12.81
°=θ→= 87.36–(leading)8.0pf
1
kVA36.87–150
1°∠=S
°=θ→= 13.53(lagging)6.0pf
3
For the line,
At the source,
2.209j7.437
LT +=+= SSS
Solution 12.82
For the delta-connected load,
pL VV =
Let I = I1 + I2 be the total line current. For I1,
For I2, convert the load to wye.
Solution 12.83
Solution 12.84
We first find the magnitude of the various currents.
For the motor,
For the capacitor,
For the lighting,
440
Consider the figure below.
If
°∠= 0Vpan
V
,
°∠= 30V3
pab
V
Ib
I2
b
n
In
a
IC
+
Ia
I1
)30(091.4
ab
1
°+θ∠==
V
I
Thus,
°∠+°∠=+= 120091.473.95249.5
C1a III
Solution 12.85
Let
RZ
Y
=
V56.138
3
240
3
V
V
L
p
===
Solution 12.86
For the single-phase three-wire system in Fig. 12.77, find currents IaA, IbB, and InN.
Figure 12.77
For Prob. 12.86.
Solution
Consider the circuit shown below.
1 Ω
1 Ω
n
b
N
B
1 Ω
a
A
In matrix form,
+
−
=
2
1
4171–
1–226
440
440
I
I
j
j
Solution 12.87
Consider the single-phase three-wire system shown in Fig. 12.78. Find the current in the
neutral wire and the complex power supplied by each source. Take Vs as a 220∠0°–V,
60-Hz source.
Figure 12.78
For Prob. 12.87.
Solution
85.18j)10x50)(60)(2(jLjmH50L
3–
==→=
πω
Consider the circuit below.
1 Ω
2 Ω
1 Ω
In matrix form,
220
20–2–23
I
232,14j775,12 +=∆
,
)8.6591975)(220(
1
j+=∆