SOLUTION

Stalling torque is torque at which speed falls to zero, i.e

N = 0

For DC shunt motor, speed is proportional to

$N \propto \frac{{{E_b}}}{\varphi }$

For stalling torque

E_b = V – I_aR_a = 0

Where,

N is the speed of the DC shunt motor

E_b is back emf

φ is flux per pole

For DC shunt motor, torque is proportional to armature current i.e. T ∝ I_a

Calculation:

Given

Total armature resistance R_a = 0.6 Ω

The full load armature current I_afull = 30 A

Terminal voltage V_DC = 240 V

Now 1Ω resistance is connected in series with armature then total resistance become

R_a = 1 + 0.6 = 1.6 Ω

During Stalling torque or the breakdown torque, the speed falls to zero

N_a ∝ E_b/φ

E_b = 0 & N_a = 0

According to voltage equation of motor

E_b = V − I_aR_a

0 = 240 − 1.6 × I_a

I_a = 150 A

∵ T ∝ φI_a (DC Motor)

T_Stalling = 150 Nm

T_Full-load = 30 Nm

The ratio of stalling to full load torque is

T_Stalling/T_Full-load  = 150/30

T_Stalling/T_Full-load  = 5