SSC JE 2011 Electrical question paper with Solution

Air gap power Pg

Pg = P_Input – stator Loss

Pg = 60 – 1 = 59 kW

Rotor copper loss = Spg

= 0.04 x 59 = 2.36 kW

Core loss = Eddy current loss + Hysteresis loss

= Kef² + Kcf

At 50 Hz, Pc = 46 watt

46 =  Ke (50)² + Kh x 50……….  1

At 70 Hz, Pc = 80 watt

70 =  Ke (70)² + Kh x 70…………… 2

From equation (1) and (2),

Ke = 0.0111

Kh = 0.363

Now at 60 Hz,

Pe = Ke x 60²

= 0.0111 x 3600 = 39.96 ≅ 40 Watt

Ph = 0.36306 x 60

= 21.78≅ 22 Watt

i= I cos (ωt + θ)

Given,

V = 4cosωt

i = 1.5cosωt – 2.598sinωt

= 1.5cosωt + 2.598sin(ωt + π/2)

Or I = Ia(cosωt + θ)……………(sinusoidal current wave)

Where Ia is amplitude or peak value of current which is given as

The use of a D-Arsonval galvanometer is very common in a variety of measuring instruments. The galvanometer is basically used in an instrument for detecting the presence of small voltages or currents in a circuit or to indicate zero current in applications lilts bridge circuits. Thus galvanometer has to be very much sensitive.

Damping: The damping is eddy current damping. The eddy currents developed in the metal former on which the coil is mounted, are responsible to produce damping torque. For effective damping, low resistance is connected across the galvanometer terminals. By adjusting the value of this resistance damping can be changed and critical damping can be achieved.

In indicating instrument the controlling torque, also called a restoring or balancing torque is obtained by two methods

1. Spring control Method
2. Gravity control Method

Spring Control Method

The springs used in measuring instruments for providing the controlling torque must have the following properties.

1. These should be of non-magnetic material.
2. Specific resistance should be low.
3. The resistance temperature coefficient should be low.
4. These should not be affected much by mechanical fatigue.

Phosphor Bronze is the most suitable for the springs of an indicating instrument as it satisfies most of the above properties. ln this method, two spiral hairsprings are used and spiraled in opposite directions. The use of two springs also avoids error due to temperature variations. One end of both the springs is attached to the body of the instrument and another end is attached to the moving system.

When the instrument is not in use, the two springs are in their natural position without any tension or compression( deflecting torque = Controlling Torque). When the instrument is connected to the circuit for the measurement, deflecting torque acts, and the pointer moves on the calibrated scale. One of the springs is unwound while the other gets twisted. The resultant movement in the springs provides the controlling torque.

More the deflection more is the twist and hence greater will be the controlling torque. Thus the controlling torque is directly proportional to the deflection of the moving system, i.e.,

Tc ∝ θ

And it is also clear that the pointer comes to rest when controlling torque becomes numerically equal to deflecting torque i.e

Tc = Td

But the deflection or the deflection torque depends upon the current flowing through it, hence

I ∝ θ

 

The Range of the DC milliammeter can be extended by using resistance in parallel. The shunts are low resistances used in ammeters for range extension. The shunt is made of Manganin or Constantan depending on whether it is used for DC or AC.

With Im as the current flow through the meter capable of producing the maximum deflection, precautions are to be taken to ensure that the current through the meter coil is limited to Im. However, when the current to be measured is large, the alternative path is provided via, the low resistance shunt Rsh.

Electrodynamic Wattmeter

The electrodynamic Wattmeter consists of a pair of fixed coils, known as current coils, and a movable coil known as the potential coil. The fixed coils are made up of a few turns of a comparatively large conductor. The potential coil consists of many turns of fine wire. The current coils are connected in series with the circuit, while the potential coil is connected in parallel.

When line current flows through the current coil of a wattmeter, a field is set up around the coil. Since for  AC power, current and voltage may not be in phase, owing to the delaying effects of circuit inductance or capacitance. Therefore the potential coil of the wattmeter generally has a high-resistance resistor connected in series with it. This is for the purpose of making the potential-coil circuit of the meter as purely resistive as possible. As a result, the current in the potential circuit is practically in phase with line voltage.

In case of DC shunt generator if we reverse the rotation there is no voltage build-up.When we rotate the generator in the reverse direction, flux due to residual magnetism will be canceled out and hence generator will not get sufficient initial flux for emf to build up.

At maximum efficiency

Core loss = Copper loss

i.e Pc = Pcu

Total loss = Pc + Pcu = 1000 watt

Pcu = 500 watt

Copper loss = X²  x Copper loss at full load

Where

X stands for loading condition of transformer

at 80% of the full load then Pcu at full load

Pcu = 500/0.8² = 781.25 watt

The inter-turn short circuit of the windings inside the rotor is a common electrical fault for the 3-phase induction motor. Bad manufacturing and assembling, overheating due to the jam in the windings, al also long-term stresses and vibrations may result in this fault. It may intensify the vibrations, burn the windings, and even lead to earth.

An inter-turn short circuit fault mainly causes the rotor to vibrate at fr (the rotating frequency of the rotor), while the static air-gap eccentricity fault primarily produces vibrations at 2fr and the combined fault generates vibrations at fr, 2fr, and 3fr at the same time which causes humming in an induction motor.