Explanation: Given a number of poles = 32. Supply frequency is 70 Hz. Rotor speed is 112 rpm. Ns = 120×f÷P=120×70÷32 = 262.5 rpm. S=Ns-Nr÷Ns = 262.5-112÷262.5=.573. F2=sf=.573×70=40.1 Hz.

Explanation: Given a number of poles = 20. Supply frequency is 90 Hz. Ns=120×f÷P=120×90÷20 = 540 rpm. S=20÷90 = .222 Hz. Nr=(1-s)Ns = 420.12 rpm. Rotor speed is 420.12 rpm.

Explanation: Sinusoidal waveform is generally expressed in the form of V=Vmsin(ωt+α) where Vm represents peak value, ω represents angular frequency, α represents a phase difference. By comparing the waveform z(t) with the generalized sinusoidal expression we can see Vm=.27 and ω=.369π rad/s.

Explanation: R.M.S value of the sinusoidal waveform is Vm÷2½ and r.m.s value of the trapezoidal waveform is Vm÷3½. The peak value of the sinusoidal waveform is Vm. The r.m.s value is Vrms = 2.11÷2½ = 1.49 V.

Explanation: No-load circuit test in an induction motor is also called an open circuit test so it is conducted at synchronous speed. Net input power taken is equal to the no-load rotational losses.

Explanation: Rotor ohmic losses are due to the resistance of armature windings. Net input power to the rotor is equal to the sum of rotor ohmic losses and mechanically developed power. Rotor ohmic losses=Air gap power-Mechanical developed power=67-26=41 KW.

Explanation: The line voltage in case of star connection is 1.73 times of phase voltage. It leads the phase voltage by an angle of 30°. VL-L=1.73×45=77.9 V.

Explanation: The slope of the V-I curve is resistance. The slope given is 1.° so R=tan(1.1°)=.019 Ω. The slope of the I-V curve is reciprocal of resistance.

Explanation: Rotor ohmic losses are due to the resistance of armature windings. Net input power to the rotor is equal to the sum of rotor ohmic losses and mechanically developed power. Rotor ohmic losses=Air gap power-Mechanical developed power=157.5-79.9=77.6 KW.

Explanation: At light loads, the current drawn is largely a magnetizing current due to the air gap and hence the power factor is low. The power factor of a squirrel cage induction motor generally is .6-.8.

Explanation: The inductor is a linear element. It only absorbs reactive power and stores it in the form of oscillating energy. The voltage and current are 90° in phase in case of the inductor so the angle between V & I is 90°. P=VIcos90° = 0 W.

Explanation: The fundamental time period of the sine wave is 2π. The time period of i(t) is L.C.M {2,2}=2 sec. The time period is independent of phase shifting and time shifting.

Explanation: The rotor resistor is a linear element. It only absorbs real power and dissipates it in the form of heat. The voltage and current are in the same phase in case of the resistor so the angle between V & I is 90°. P=I2R=.65×.65×14.23=6.01 W.

Explanation: Mark to space is Ton÷Toff. It is the ratio of time for which the system is active and the time for which is inactive. M = Ton÷Toff = 4.3÷78.2 = .054.