# A 250 V, DC shunt motor takes a line current of 20 A. The resistance of shunt field winding is 200Ω and resistance of the armature is 0.3 Ω Find the armature current and the back EMF.

A 250 V, DC shunt motor takes a line current of 20 A. The resistance of shunt field winding is 200Ω and resistance of the armature is 0.3 Ω Find the armature current and the back EMF.

### Right Answer is:

18.75 A, 245 V

#### SOLUTION

Supply Voltage **V** = 250 V

Line Current **I _{L}** = 20A

Shunt Resistance

**R**= 200Ω

_{sh}Armature Resistance

**R**= 0.3 Ω

_{a}Armature Current

**I**=?

_{a}Back EMF

**E**=?

_{b}The Diagram of the given question is shown in figure

**(i) Armature current**

The Line current of DC shunt motor is the sum of Armature current and Shunt field current

**I _{L} = I_{a} + I_{sh}**

And Shunt Field Resistance is given as

**I _{sh} = V/R_{sh}** = 250/200 =

**1.25 A**

∴ I_{a} = I_{L} − I_{sh}

**I _{a} = 20 − 1.25 = 18.75 A**

**(ii) Back EMF**

The Back EMF of DC Motor is given by

**E _{b} = V − I_{a}R_{a}**

= 250 − 18.75 × 0.3

= 250 − 5.625

**= 244.375 V ≅ 245 V**