Question

. A shunt generator delivers 50 kW at 250 V and runs at 400 rpm. The armature and field resistances are 0.02 Ω and 50 Ω respectively. Calculate the speed of the machine running as a shunt motor and taking 50 kW input at 250 V. Allow 1 V per brush for contact drop.

Answer 1

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Answer 2

The speed of the machine running as a shunt motor and taking 50 kW input at 250 V is 382 rpm.

Given : A shunt generator delivers 50 kW at 250 V and runs at 400 rpm

Resistance of armature is 0.02 ohm

Resistance of field is 50 ohm

Voltage of 1 V per brush for contact drop

To Find : The speed of the machine running as a shunt motor and taking 50 kW input at 250 V.

Solution :  The speed of the machine running as a shunt motor and taking 50 kW input at 250 V is 382 rpm.

It is given that a shunt generator delivers 50 kW at 250 V and runs at 400 rpm , the armature and field resistances are 0.02 Ω and 50 Ω respectively and Voltage of 1 V per brush for contact drop

We have to find the speed of the machine running as a shunt motor and taking 50 kW input at 250 V.

We know that Power = Voltage × Current

P = V × I

The load current (I1) of the generator is

I1= $\frac{P}{V}$

Power (P) is 50 kW = 50000 W

Voltage is 250 V

So I1 = $\frac{50000}{250}$

= 200 A

So load current is 200 A

Now we know that

V = IR

So field current is

I2 = $\frac{V}{R}$

Voltage (V) is 250 V

Resistance (R) is 50 ohm

I2 = $\frac{250}{50}$

= 5 A

So field current is 5 A

Now armature current is sum of load current and field current

I1+I2

= 200+5

=205 A

Armature drop is R × I  

= 0.02 × 205

= 4.1 V

Hence induced emf inducting brush drop is

250 +4.1+2

= 256.1 volt

When input to motor is 50 kW , the line current is 200 A and since field current is 5 A ,

the armature current is 200-5 = 195 A

Now armature drop will be I × R

195 × 0.02

= 3.9 V

The net back emf will be 250 - 3.9 - 2

= 244.1 V

Hence speed of a machine running as a shunt motor is $\frac{244.1}{256.1}$ × 400

= 382 rpm.

So speed of the machine running as a shunt motor and taking 50 kW input at 250 V is 382 rpm.

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