---
title: "Starting current and rotor resistance for 150 kW slip ring motor"
subject: "Electrical Machines I"
chapter: 5
key: "semester_4/electrical_machines_i:im-150kw-3000v-starting-current-30a"
source: https://www.bctengineer.com/q/semester_4/electrical_machines_i/im-150kw-3000v-starting-current-30a
site: BCT Engineering
---

# Starting current and rotor resistance for 150 kW slip ring motor

Electrical Machines I · Chapter 5: Three-Phase Induction Machines

- Asked in: 2070 Bhadra, 8 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machines_i/im-150kw-3000v-starting-current-30a
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines_i/chapter-5

## Question

A 150 kW, 3000 V, 50 Hz, 4 pole star-connected induction motor has a star-connected slip ring rotor with a transformation ratio of 4 (stator to rotor). The rotor resistance is 0.1 ohm/phase and rotor inductance is 3.61 mH per phase. Neglecting the stator impedance, calculate: a) Starting current on rated voltage with slip rings short circuited. b) Necessary external resistance to be connected in rotor side to reduce starting current to 30 A.

## Short answer

Stator phase voltage 1732 V, rotor standstill E2 = 433 V, X2 = 1.134 Ω. Short‑circuit rotor current 380.3 A gives stator starting current 95.1 A. To limit stator current to 30 A, rotor current 120 A needs external resistance 3.33 Ω per phase.

## Answer

**Given:** 150 kW, 3000 V (star), 50 Hz, 4 poles, slip-ring rotor (star), stator/rotor ratio $= 4$, $R_2 = 0.1\ \Omega$, $L_2 = 3.61$ mH per phase. Stator impedance neglected.

#### Rotor quantities at standstill

$$
\begin{aligned}
E_1 &= \frac{3000}{\sqrt{3}} = 1732.05\ \text{V/phase} \\
E_2 &= \frac{E_1}{4} = 433.01\ \text{V/phase} \\
X_2 &= 2\pi f L_2 = 2\pi \times 50 \times 3.61\times10^{-3} = 1.1341\ \Omega \\
Z_2 &= \sqrt{0.1^2 + 1.1341^2} = 1.1385\ \Omega
\end{aligned}
$$

#### (a) Starting current with slip rings shorted

$$
\begin{aligned}
I_{2,st} &= \frac{E_2}{Z_2} = \frac{433.01}{1.1385} = 380.3\ \text{A (rotor)} \\
I_{1,st} &= \frac{I_{2,st}}{4} = \frac{380.3}{4} = 95.08\ \text{A (stator/line)}
\end{aligned}
$$

#### (b) External resistance to limit starting current to 30 A

Taking 30 A as the stator (line) current, the rotor current must be:

$$
I_2 = 30 \times 4 = 120\ \text{A}
$$

$$
\begin{aligned}
Z_{2,new} &= \frac{433.01}{120} = 3.6084\ \Omega \\
R_{total} &= \sqrt{Z_{2,new}^2 - X_2^2} = \sqrt{3.6084^2 - 1.1341^2} = 3.4256\ \Omega \\
R_{ext} &= R_{total} - R_2 = 3.4256 - 0.1 = 3.3256\ \Omega
\end{aligned}
$$

**Answer: (a) starting current $\approx 95.1$ A in the stator (380.3 A in the rotor); (b) external resistance $\approx 3.33\ \Omega$ per phase in the rotor circuit.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is the rotor emf per phase at standstill?
   A. E2 = (3000/sqrt3)/4 = 433 V
   B. E2 = 3000/4 = 750 V
   C. E2 = 3000 x 4/sqrt3 = 6928 V
   D. E2 = 3000/sqrt3 = 1732 V
   Answer: A. Stator phase voltage is 1732 V; dividing by the transformation ratio 4 gives 433 V. (Key point: Rotor standstill emf)

2. How is the stator starting current found with slip rings shorted?
   A. I = 3000/Z2 = 2635 A
   B. I2 = E2/Z2 = 380.3 A in the rotor, divided by 4 gives 95.1 A
   C. I2 = E2/R2 = 4330 A
   D. I1 = 380.3 x 4 = 1521 A
   Answer: B. Rotor current is E2/sqrt(R2^2 + X2^2) = 380.3 A; the stator carries 1/4 of it. (Key point: Starting current)

3. To limit the stator current to 30 A, what rotor current is needed?
   A. 7.5 A
   B. 30 A
   C. 120 A
   D. 520 A
   Answer: C. Rotor current is the stator current multiplied by the ratio 4: 30 x 4 = 120 A. (Key point: Rotor current for 30 A)

4. How is the external resistance computed?
   A. R_ext = 433/120 = 3.61 ohm
   B. R_ext = sqrt(Z^2 + X2^2) = 3.78 ohm
   C. R_ext = Z - X2 = 2.47 ohm
   D. R_total = sqrt(Z^2 - X2^2) with Z = 433/120, then subtract R2: about 3.33 ohm
   Answer: D. Reactance stays fixed; only resistance changes, so R_total = 3.4256 ohm and R_ext = 3.4256 - 0.1 = 3.33 ohm. (Key point: External resistance)

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