# A 240v dc shunt motor with an armature resistance of 0.5  has a full load current of 40A. Find out the ratio of the stalling torque to the full load torque when resistance of 1 ohm is connected in series with the armature

A 240v dc shunt motor with an armature resistance of 0.5  has a full load current of 40A. Find out the ratio of the stalling torque to the full load torque when resistance of 1 ohm is connected in series with the armature

#### SOLUTION

Stalling torque is the torque at which speed would fall to zero.

With N = 0 , Eb = 0

Hence the value of armature current

From the voltage equation, the back EMF of DC motor at no-load

Eb = V − IaRa

Since external resistance, Rext is added in series with the motor. Hence

Eb = V − Ia(Ra + Rext)

0 = 240 − Ia(0.5 + 1)

Ia = 220 ⁄ 1.5

Ia = 160 A

The torque developed by a d.c motor is directly proportional to Flux per pole × Armature Resistance i.e

T ∝ ΦI(Now flux is constant hence )
T ∝ Ia

Hence Ratio of stalling torque to full load torque will be

T2 ⁄ T1 = I2 ⁄ I1

T2 ⁄ T1 = 160/40 = 4

T2 ⁄ T1 = 4

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