A 10 k W, 250 V D C self excited shunt generator driven at 1000 rpmhas armature resistance 0.15 ohm and field current 1.64 A. Find rated load, armature induced emf, torque developed and efficiency when the rotational losses are 540 watt. Assume constant speed operation.

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[latex] ext { Here, } \quad ext { output power }=10 kW =10 imes 1000 W[/latex]

[latex]R_{a}=0.15 \Omega ; I_{s h}=1.64 A ; V=250 V ; N=1000 rpm[/latex]

[latex] ext { Load current, } I_{L}=\frac{10 imes 1000}{250}=40 A [/latex]

[latex] ext { Armature current, } I_{a}=I_{L}+I_{s h}=40+1.64=41.64 A[/latex]

[latex] ext { Induced or generated emf, } E_{g}=V+I_{a} R_{a}[/latex]

[latex]=250+41.64 imes 0.15=256.246 V [/latex]

[latex] ext { Power developed in the armature, } \quad \omega T=E_{g} I_{a}[/latex]

[latex]\begin{array}{l} herefore\ ext { Torque developed, } T=\frac{E_{g} I_{a}}{\omega}=\frac{256 \cdot 246 imes 41 \cdot 64 imes 60}{2 \pi imes 1000} \quad\left( ext { since } \omega=\frac{2 \pi N}{60} ight)\end{array}[/latex]

[latex]=101.89 Nm [/latex]

[latex] ext { Power developed }=E_{g} I_{a}=256.246 imes 41.64=10670 W[/latex]

[latex]\begin{aligned} ext { Mechanical losses } &=540 W \ ext { Power input } &=10670+540=11210 W \ ext { Power output } &=10 kW =10 imes 1000 W \ ext { Efficiency, } \eta &=\frac{ ext { output }}{ ext { input }} imes 100=\frac{10 imes 1000}{11210} imes 100= 8 9.2 \% \end{aligned}[/latex]

Question 5.42: A 10 k W, 250 V D C self excited shunt generator driven at 1...

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