With 0.5 kW of friction and windage, that machine's shaft output is
Answer: A
Correct answer: 26.66 kW
The mechanical power developed is the air gap power less the rotor copper loss, \( 28 - 0.84 = 27.16 \) kW, and the shaft output is that less friction and windage: \[ 27.16 - 0.5 = 26.66\ \mathrm{kW}. \] Against a 30 kW input the efficiency is 88.9 per cent.
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An induction machine develops 80 N·m at 5 per cent slip on a 1,500 rpm synchronous speed. Its air gap power is nearest
Answer: B
Correct answer: 12.6 kW
Air gap power is the torque multiplied by the synchronous angular velocity, not the actual one: \[ \omega_s = \frac{2\pi \times 1500}{60} = 157.1\ \mathrm{rad/s}, \qquad P_g = 80 \times 157.1 = 12{,}566\ \mathrm{W}. \] The slip does not enter this calculation; it determines how the 12.6 kW then divides between rotor loss and mechanical power.
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A machine whose rotor resistance is doubled will have its slip at maximum torque
Answer: C
Correct answer: doubled
The slip at which torque peaks is \( s = R_2/X_2 \), so doubling the rotor resistance doubles it. The peak torque itself is unchanged, since it depends on the voltage and the standstill reactance alone - which is precisely why external rotor resistance is useful: it moves the peak towards standstill and so raises the starting torque without altering its magnitude.
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A machine with 4 per cent full-load slip is operated at 90 per cent of rated voltage with the same load torque. Its slip becomes about
Answer: D
At small slip the torque is proportional to slip and to the square of the voltage, so holding the torque requires the slip to rise as the inverse square, giving \( 0.04/0.81 = 0.049 \). Extra slip means extra rotor loss and a hotter machine.
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Consider the following statements about the equivalent circuit.
1. Rotor resistance appears divided by slip.
2. Rotor reactance appears at its standstill value.
3. The magnetising branch carries the load current.
Which are correct?
Answer: A
The first two are the two adjustments that referring to supply frequency requires. The magnetising branch carries only the current that establishes the flux and supplies the core loss, which is why it sits across rather than in series with the rotor branch.
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Consider the following statements about torque.
1. Maximum torque is independent of rotor resistance.
2. Starting torque rises with rotor resistance up to a point.
3. Torque follows the square of the applied voltage.
Which are correct?
Answer: B
All three are standard results, and together they explain both why rotor resistance starting works and why reduced-voltage starting costs so much torque. The point beyond which added resistance reduces starting torque is where the peak has passed standstill.
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Match the test with what it yields.
1. No-load test 2. Blocked rotor test 3. Direct current test
P. Stator resistance Q. Series impedance R. Magnetising parameters
Answer: C
Correct answer: 1-R, 2-Q, 3-P
Three tests, three parts of the equivalent circuit. The no-load test runs the machine unloaded, where the slip is nearly zero and almost all the current is magnetising, so it yields the shunt branch. The blocked rotor test short-circuits the machine and yields the series impedance. And a direct current measurement, which involves no flux at all, gives the stator resistance on its own.
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Match the rotor type with its property.
1. Cage 2. Wound 3. Double cage
P. External resistance can be inserted Q. High starting torque with low running slip R. Simplest and most robust construction
Answer: D
Each construction trades simplicity against control, and the double cage recovers much of the wound rotor's starting behaviour without any brushes. Which is chosen depends on whether the rotor circuit ever needs to be reached.
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Assertion (A): A three-phase induction motor is self-starting.
Reason (R): Its stator produces a revolving field of constant magnitude.
Select the correct option.
Answer: A
Correct answer: Both A and R are true, and R is the correct explanation of A
Both are true and the reason gives the mechanism. Three currents displaced by 120 degrees in time, flowing in three windings displaced by 120 degrees in space, produce a resultant of constant magnitude revolving at synchronous speed. That field cuts the stationary rotor at once, inducing current and producing torque without any starting arrangement - which the single-phase machine, whose field merely pulsates, does require.
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Assertion (A): Adding rotor resistance does not change the maximum torque.
Reason (R): The peak torque depends on the voltage and the standstill reactance alone.
Select the correct option.
Answer: B
Correct answer: Both A and R are true, and R is the correct explanation of A
Both are true and the reason gives the mechanism. The maximum torque works out as \( kV^2/(2X_2) \), in which the rotor resistance does not appear. Adding resistance moves the peak to a higher slip without changing its height, so the starting torque rises while the breakdown torque stays where it was.
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