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A 200-V, DC motor has an armature resistance of 0.5 ╬й. It is drawing an armature current of 20 A driving a certain load. Calculate the induced EMF in the motor under this condition.
175.8 V
203.7 V
190 V
199.3 V
190 V
The induced EMF (EbтАЛ) in a DC motor is the back EMF that opposes the applied terminal voltage (V). It is calculated using the voltage balance equation across the armature circuit, considering the armature resistance voltage drop.
IS 4889:1968
The induced EMF (EbтАЛ) in a DC motor is the back EMF that opposes the applied terminal voltage (V). It is calculated using the voltage balance equation across the armature circuit, considering the armature resistance voltage drop.
V=EbтАЛ+IaтАЛRaтАЛ тАФ Basic voltage balance equation
EbтАЛ=VтИТIaтАЛRaтАЛ тАФ Formula to calculate back EMF
When a DC voltage is applied to the motor terminals, the armature current IaтАЛ flows through the armature resistance RaтАЛ. According to Kirchhoff's Voltage Law, the applied voltage V must overcome the internal voltage drop IaтАЛRaтАЛ and the back EMF EbтАЛ produced by the rotation of the armature conductors in the magnetic field.
The back EMF is always less than the applied voltage in a motoring mode.
The power loss in the armature is given by Ia2тАЛRaтАЛ.
Back EMF is proportional to the speed of the motor and the magnetic flux.
Provides inherent self-regulation for motor speed.
Limits the armature current during steady-state operation.
Requires an external starter to limit initial high current during start-up when EbтАЛ=0.
Sensitive to variations in supply voltage.
Industrial DC drives
Variable speed control systems
Calculation: Given V=200┬аV, IaтАЛ=20┬аA, RaтАЛ=0.5╬й. Then EbтАЛ=200тИТ(20├Ч0.5)=200тИТ10=190┬аV.
Option A is incorrect as it assumes a larger voltage drop. Option B is incorrect as it represents V+IaтАЛRaтАЛ (generator mode). Option D assumes a smaller, incorrect calculation.
C is correct тАФ The induced EMF (back EMF) is calculated as 190┬аV using the equation EbтАЛ=VтИТIaтАЛRaтАЛ.
Always remember that in a DC motor, V>EbтАЛ, whereas in a DC generator, EgтАЛ>V. This sign convention is critical for avoiding errors in power flow analysis.
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