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A 3-φ induction motor having a star-connected rotor has an induced e. m.f. of 80 volts between slip-rings at standstill on open-circuit. The rotor has a resistance and reactance per phase of 1 Ω and 4 Ω respectively. Calculate current/phase and power factor when  slip-ring, are short-circuit

Rotor induced E.M.F per phase on standstill condition, E2 = 80 V
Rotor resistance per phase, R2 = 1 Ω
Rotor reactance per phase, X2 = 4 Ω

As the rotor windings are star-connected, the induced E.M.F. per phase on the rotor circuit, E2 per phase, is given by:

E2 per phase = E2/√3 = 80/√3 = 46.2 V

The rotor impedance per phase, Z2, is given by:

Z2 = √(R22 + X22) = √(12 + 42) = 4.12 Ω

The rotor current per phase, I2 per phase, when the slip-rings are short-circuited, is given by:

I2 per phase = E2 per phase / Z2 = 46.2 / 4.12 = 11.2 A

The power factor of the rotor circuit, cos(φ2), is given by:

cos(φ2) = R2 / Z2 = 1/4.12 = 0.243

Therefore, the current per phase is 11.2 A, and the power factor is 0.243 when the slip-rings are short-circuited.