Question 7.6: A dc shunt generator delivers 12 kW at 240 V while running a...
A dc shunt generator delivers 12 kW at 240 V while running at 1500 rpm. Calculate the speed of the machine when running as a shunt motor and taking 12 kW at 240 V. The armature resistance is 0.1 Ω and field resistance is 80 Ω.
As a generator,
\begin{aligned}I_{f} &=\frac{V}{R_{f}}=\frac{240}{80}=3 A \\ I_{L} &=\frac{12 \times 1000}{240}=50 A \\ I_{a} &=I_{L}+I_{f}=50+3=53 A \\ E_{g} &=V+I_{a} R_{a}=240+53 \times 0.1 \\ &=245.3 V\end{aligned}As a motor,
\begin{aligned}I_{L} &=I_{a}+I_{f} \\ I_{a} &=I_{L}-I_{f} \\ I_{L} &=\frac{12 \times 1000}{240}=50 A, \quad I_{f}=\frac{V}{R_{f}}=\frac{240}{80}=3 A \\ I_{a} &=50-3=47 A \\ E_{m} &=V-I_{a} R_{a}=240-47 \times 0.1 \\&=235.3 V\end{aligned}Let the speed of the machine as generator be N_{1} and as motor be N_{2}
E_{g} =\frac{\phi Z N_{1} P}{60 A} \text { and } E_{m}=\frac{\phi Z N_{2} P}{60 A}or, \frac{E g}{E m} =\frac{N 1}{N 2}
or, N_{2} =N_{1} \frac{E m}{E g}=1500 \times \frac{235.3}{245.3}=1439 rpm.
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