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614 ⏐⏐⏐ THE BASIC ELEMENTS AND PHASORS
EXAMPLE 14.30 Write the sinusoidal expression for the following
phasors if the frequency is 60 Hz:
Phasor Domain Time Domain
a. I � 10 �30° i � �2�(10) sin(2p60t � 30°)
and i � 14.14 sin(377t � 30°)
b. V � 115 ��70° v � �2�(115) sin(377t � 70°)
and v � 162.6 sin(377t � 70°)
EXAMPLE 14.31 Find the input voltage of the circuit of Fig. 14.65 if
va � 50 sin(377t � 30°)
vb � 30 sin(377t � 60°)
⎫
⎬
⎭
f � 60 Hz
+
–
e in
+ –
v a
FIG. 14.65
Example 14.31.
Solution: Applying Kirchhoff’s voltage law, we have
ein � va � vb Converting from the time to the phasor domain yields
va � 50 sin(377t � 30°) ⇒ Va � 35.35 V �30°
vb � 30 sin(377t � 60°) ⇒ Vb � 21.21 V �60°
Converting from polar to rectangular form for addition yields
Va � 35.35 V �30° � 30.61 V � j 17.68 V
Vb � 21.21 V �60° � 10.61 V � j 18.37 V
Then
Ein � Va � Vb � (30.61 V � j 17.68 V) � (10.61 V � j 18.37 V)
� 41.22 V � j 36.05 V
Converting from rectangular to polar form, we have
Ein � 41.22 V � j 36.05 V � 54.76 V �41.17°
Converting from the phasor to the time domain, we obtain
Ein � 54.76 V �41.17° ⇒ ein � �2�(54.76) sin(377t � 41.17°)
and ein � 77.43 sin(377t � 41.17°)
+
v b
–
�