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SSC JE Electrical 2019 with solution SET-1
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Two coupled coils with L1 = L2 = 0.5H have a coupling coefficient of K = 0.75. The turn ratio N1 ⁄ N2 = ?

The self-inductance is given as

L = μN2A/I

L ∝ N2

where

N is the number of turns of the solenoid

A is the area of each turn of the coil

l is the length of the solenoid

and μ is the permeability constant

L1/L2 = N21/N22

0.5/0.5 = N21/N22

N1/N2 = 1

SSC JE Electrical 2019 with solution SET-1
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Let T be the net torque developed by the rotor runs at ω rad/s. What is the mechanical power developed?

By the term, torque is meant the turning or twisting moment of a force about an axis. It is measured by the product of the force and the radius at which this force acts. Consider a pulley of radius r meter acted upon by a circumferential force of F Newton which causes it to rotate at N r.p.m.

The angular speed of the pulley is

ω = 2πN/60 rad/sec

Work is done by this force in one revolution

= Force × distance = F × 2πR Joule

The power developed = Work Done/Time

= (F × 2πR)/60/N

= (F × R) × (2πN)/60

The power developed = T × ω watt or P = T ω Watt

pmech = (ωT)

SSC JE Electrical 2019 with solution SET-1
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The laws involved in the expression e = −dφ/dt are

Faraday’s 1st laws of electromagnetic induction tell us about the condition under which an e.m.f. is induced in a conductor or coil a when the magnetic flux linking a conductor or coil changes.

Faraday’s 2nd laws of electromagnetic induction give the magnitude of the induced e.m.f in a conductor or coil and may be stated as:

The magnitude of the e.mf induced in a conductor or coil is directly proportional to the rate of change of magnetic flux linkages.

Suppose a coil has N turns and magnetic flux linking the coil increases (i.e. changes) from φ1 Wb to φ2 Wb in t seconds. Now, magnetic flux linkages mean the product of magnetic flux and the number of turns of the coil.

N = e dφ/dt

Lenz Law:- Lenz’s law states: the direction of the induced e.m.f. is such as to oppose the change producing it. Therefore, the magnitude and direction of induced e.m.f. should be written as :

N = −e dφ/dt

SSC JE Electrical 2019 with solution SET-1
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Find the frequency of rotor induced EMF of a 3-phase, 440V, 50 Hz induction motor has a slip of 10%

Given Data

Voltage = 440 V

Frequency = 50 Hz

Slip = 10% =0.1

Now,

Rotor frequency = slip × frequency

= 0.1 × 50 = 5 Hz