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?a)68.13 Ab)65.06 Ac)70.16 Ad)74.07 ACorrect answer is option 'B'. Can you explain this answer?

Question

A 3 &ndash; 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 &Omega; respectively at standstill. What is the rotor current per phase at rotor developing maximum torque?a)68.13 Ab)65.06 Ac)70.16 Ad)74.07 ACorrect answer is option 'B'. Can you explain this answer?

Answer

We have, R₂ = 0.5 Ω, X₂ = 2.5 Ω
At maximum torque, R₂ = sX₂
Where s is the slip.

Impedance at maximum torque,

= 0.707 Ω (∵ Xr = sX2)
Standstill phase voltage in rotor is
E2=230V ( ∵ Delta connection)
Now rotor induced emf is
E_r=sE₂=0.2×230
= 46 V
Rotor current per phase,

Answer

We have, R₂ = 0.5 Ω, X₂ = 2.5 Ω
At maximum torque, R₂ = sX₂
Where s is the slip.

Impedance at maximum torque,

= 0.707 Ω (∵ Xr = sX2)
Standstill phase voltage in rotor is
E2=230V ( ∵ Delta connection)
Now rotor induced emf is
E_r=sE₂=0.2×230
= 46 V
Rotor current per phase,

Answer

- **Calculating Rotor Current at Maximum Torque**
- **Formula Used:**
The formula used to calculate rotor current at maximum torque is:
$$
I_{2} = \frac{V_{s}}{Z_{s} + jX_{s}}
$$
- **Given Data:**
- Induced emf at standstill, $V_{s} = 230 V$
- Resistance at standstill, $R_{s} = 0.5 \Omega$
- Leakage reactance at standstill, $X_{s} = 2.5 \Omega$
- **Calculations:**
1. Calculate the impedance at standstill:
$$
Z_{s} = R_{s} + jX_{s} = 0.5 + j2.5 = 0.5 + j2.5 \Omega
$$
2. Substitute the values in the formula to calculate rotor current at maximum torque:
$$
I_{2} = \frac{230}{0.5 + j2.5} = \frac{230}{\sqrt{0.5^{2} + 2.5^{2}}} \angle \arctan{\left(\frac{2.5}{0.5}\right)} = \frac{230}{\sqrt{6.25}} \angle \arctan{5} = \frac{230}{2.5} \angle 78.69^{\circ} = 65.06 A \angle 78.69^{\circ}
$$
- **Final Answer:**
The rotor current per phase at rotor developing maximum torque is approximately $65.06 A$.

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