A separately excited DC motor at rated field drives a fan at 1000 rpm with armature voltage 100 V and current 10 A. Ra=1 Ω and fan torque is proportional to speed squared. Neglect rotational losses. Find voltage for 500 rpm.
Initially back emf is 100−10(1)=90 V. At unchanged field it is proportional to speed, so halving speed makes the back emf 45 V.
Fan torque falls with speed squared to one quarter. Motor torque at fixed field is proportional to armature current, so new current is 10/4=2.5 A.
Required voltage is E+IaRa=45+2.5=**47.5 V**.
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