A 2500 V, 50 Hz delta connected induction motor has a star connected slip ring rotor with a phase transformation ratio of 3.5. At standstill, the rotor resistance and leakage reactance are 0.04 and 0.6 Ω respectively. What is the value of rotor current at 4% slip with slip rings shorted?a)714.286 Ab)613.1 Ac)2145.85 Ad)None of theseCorrect answer is option 'B'. Can you explain this answer?

Question

A 2500 V, 50 Hz delta connected induction motor has a star connected slip ring rotor with a phase transformation ratio of 3.5. At standstill, the rotor resistance and leakage reactance are 0.04 and 0.6 &Omega; respectively. What is the value of rotor current at 4% slip with slip rings shorted?a)714.286 Ab)613.1 Ac)2145.85 Ad)None of theseCorrect answer is option 'B'. Can you explain this answer?

Answer

Rotor phase voltage at standstill,

R₂ = 0.04 Ω
X₂ = 0.6 Ω
X_r = sX₂ = 0.04 × 0.6
= 0.024 Ω
E_r = sE₂
= 0.04 × 714.286 V
= 28.57 V

Answer

Rotor phase voltage at standstill,

R₂ = 0.04 Ω
X₂ = 0.6 Ω
X_r = sX₂ = 0.04 × 0.6
= 0.024 Ω
E_r = sE₂
= 0.04 × 714.286 V
= 28.57 V

Answer

Respectively. The stator winding resistance and leakage reactance are 0.05 and 0.8 respectively. The rated stator current is 100 A.

To find the full-load slip of the motor, we can use the formula:

Slip = (Ns - Nr) / Ns

Where:
Ns = synchronous speed
Nr = rotor speed

The synchronous speed can be calculated using the formula:

Ns = (120 * f) / P

Where:
f = frequency
P = number of poles

Given:
f = 50 Hz
P = 3 (delta connected)

Ns = (120 * 50) / 3
Ns = 2000 rpm

Since the motor is at standstill, Nr = 0.

Slip = (2000 - 0) / 2000
Slip = 1

The full-load slip of the motor is 1.

To find the full-load rotor current, we can use the formula:

I2 = (s * Ir) / (s + 1)

Where:
I2 = rotor current
Ir = rated stator current
s = slip

Given:
Ir = 100 A
s = 1 (full-load slip)

I2 = (1 * 100) / (1 + 1)
I2 = 50 A

The full-load rotor current is 50 A.

To find the full-load rotor copper loss, we can use the formula:

Prcl = 3 * I2^2 * Rr

Where:
Prcl = rotor copper loss
I2 = rotor current
Rr = rotor resistance

Given:
I2 = 50 A
Rr = 0.04

Prcl = 3 * (50^2) * 0.04
Prcl = 300 * 0.04
Prcl = 12 kW

The full-load rotor copper loss is 12 kW.

To find the full-load rotor output, we can use the formula:

Pout = Prcl / (1 - s)

Where:
Pout = rotor output
Prcl = rotor copper loss
s = slip

Given:
Prcl = 12 kW
s = 1 (full-load slip)

Pout = 12 / (1 - 1)
Pout = 12 / 0
Pout = undefined

The full-load rotor output is undefined because the denominator becomes zero.

Please note that the calculations provided are based on the given information and assumptions.

Similar Electrical Engineering (EE) Doubts

A 2500 V, 50 Hz delta connected induction motor has a star connected slip ring rotor with a phase transformation ratio of 3.5. At standstill, the rotor resistance and leakage reactance are 0.04 and 0.6 Ω respectively. What is the value of rotor current at 4% slip with slip rings shorted?

A 3 – phase, slip ring induction motor with delta connected rotor has an induced emf of 230 V between slip rings at standstill. Resistance and leakage reactance are 0.5 and 2.5 Ω respectively at standstill. What is the rotor current per phase at rotor developing maximum torque?

The rotor resistance and standstill reactance of a 3-phase induction motor are respectively 0.018Ω and 0.08 Ω per phase, normal slip at full load is 4%. The percentage reduction in stator voltage to develop full-load torque at half of full-load speed is.

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