Question

A 3-phase, slip-ring, induction motor with star-connected rotor has an induced e.m.f. of 120 volts between slip-rings at standstill with normal voltage applied to the stator. The rotor winding has a resistance per phase of 0.3 ohm and standstill leakage reactance per phase of 1.5 ohm. Calculate (i) rotor current/phase when running short-circuited with 4 percent slip and (ii) the slip and rotor current per phase when the rotor is developing maximum torque.

Answer 1

To calculate the rotor current/phase when running short-circuited with 4 percent slip, use the formula: Rotor current/phase = (Induced e.m.f. / (Rotor resistance + Slip x Standstill leakage reactance per phase)). To find the slip and rotor current/phase when the rotor is developing maximum torque, use the formula: Slip = ((Rotor resistance / (Standstill leakage reactance / 2)) + 1) / ((Rotor resistance / (Standstill leakage reactance / 2)) + 2) and Rotor current/phase = (Induced e.m.f. / (Rotor resistance + slip x Standstill leakage reactance per phase)).

Step-by-step explanation:

To find the rotor current per phase when running short-circuited with 4 percent slip, we need to use the formula:

Rotor current per phase = (Induced e.m.f. / (Rotor resistance + Slip x Standstill leakage reactance per phase))

Plugging in the given values, we get:

Rotor current per phase = (120 V / (0.3 Ω + 0.04 x 1.5 Ω)) = 114.286 A

Therefore, the rotor current per phase when running short-circuited with 4 percent slip is 114.286 A.

To find the slip and rotor current per phase when the rotor is developing maximum torque, we need to use a different formula. The slip is given by:

Slip = ((Rotor resistance / (Standstill leakage reactance / 2)) + 1) / ((Rotor resistance / (Standstill leakage reactance / 2)) + 2)

Plugging in the given values, we get:

Slip = ((0.3 Ω / (1.5 Ω / 2)) + 1) / ((0.3 Ω / (1.5 Ω / 2)) + 2) = 0.4167

The rotor current per phase when the rotor is developing maximum torque can be found using the formula:

Rotor current per phase = (Induced e.m.f. / (Rotor resistance + slip x Standstill leakage reactance per phase))

Plugging in the given values, we get:

Rotor current per phase = (120 V / (0.3 Ω + 0.4167 x 1.5 Ω)) = 61.538 A

Therefore, the slip when the rotor is developing maximum torque is 0.4167 and the rotor current per phase is 61.538 A.