Question 22.7: For a transformer having the equivalent circuit in Fig. 22.2...
For a transformer having the equivalent circuit in Fig. 22.20:
a. Determine R_{e} \text { and } X_{e} .
b. Determine the magnitude of the voltages V_{L} \text { and } V_{g}.
c. Determine the magnitude of the voltage V_{g} to establish the same load voltage in part (b) if R_{e} \text { and } X_{e}=0 \Omega . Compare with the result of part (b).
\text { a. } R_{e}=R_{p}+a^{2} R_{s}=1 \Omega+(2)^{2}(1 \Omega)=5 \Omega.
X_{e}=X_{p}+a^{2} X_{s}=2 \Omega+(2)^{2}(2 \Omega)= 1 0 \Omega.
b. The transformed equivalent circuit appears in Fig. 22.21.
a V_{L}=\left(I_{p}\right)\left(a^{2} R_{L}\right)=2400 V.
Thus,
V_{L}=\frac{2400 V }{a}=\frac{2400 V }{2}=1200 V.
and
V _{g}= I _{p}\left(R_{e}+a^{2} R_{L}+j X_{e}\right).
=10 A (5 \Omega+240 \Omega+j 10 \Omega)=10 A (245 \Omega+j 10 \Omega).
V _{g}=2450 V +j 100 V =2452.04 V \angle 2.34^{\circ}.
=2452.04 V \angle 2.34^{\circ}.
\text { c. For } R_{e} \text { and } X_{e}=0, V_{g}=a V_{L}=(2)(1200 V )=2400 V \text {. }Therefore, it is necessary to increase the generator voltage by 52.04 V (due to R_{e} \text { and } X_{e} \text { ) } to obtain the same load voltage.
