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Question

# A dc series motor is driving a fan load where the load torue is proportional to square of speed. The rsistance of armature and field are 0.03 Ω and 0.05 Ω respectively. If the motor takes 15 A and runs at 1500 rpm with supply voltage of 200 V. The value of resistance to be added in series with the armature to reduce the speed to 750 rpm, is ______

A
20.04 Ω
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B
20.12Ω
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C
19.88Ω
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D
19.96 Ω
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Solution

## The correct option is D 19.96 ΩLoad characteristic is TLαN2 For dc series motor, torque-currrent relation is given by TdαI2a ∴Ia2Ia1=N2N1 Ia215=7501500 Ia2=7.5A Case-I: Ea1=200−15×(0.03+0.05) Ea1=198.8V Case-II: When additional resistance added in series with the armature circuit, Ia2=7.5A, N2=750rpm Now, Eaαϕωm Ea2Ea1=N2N1Ia2Ia1 (In dc series motor ϕ∞Ia) Ea2198.8=750×7.51500×15 Ea2=49.7V Ea2=200−7.5(0.08+Rext)=49.7 0.08+Rext=200−49.77.5 Rext=20.04−0.08 =19.96Ω

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