The energy stored in the magnetic field of an inductor can be expressed as

E = 1/2L I²

where

E = energy stored (joules, J)

L = inductance (henrys, H)

I = current (amps, A)

1/2(100 × 10^-3 × 1)

50 × 10^-3 J

0.05 J

Here L = 4H and di/dt = 2 A

Hence voltage Across inductor

= V = L(di/dt)

= 4 x 2 = 8 V

The amplitude of the current in a pure inductive circuit is given by

Im = Vm/ωl

And ω = 2πf

Im = Vm/2πfl

Im ∝ 1/f

Hence, when the frequency is halved, the amplitude of the current is doubled in a pure inductive circuit.

Number of poles of alternator Pa = 10

F = 25 Hz (alternator)

F = 60 Hz (motor)

Then the number of poles of motor Pm =?

Since the synchronous motor is directly coupled hence

Synchronous speed of an alternator = Synchronous speed of the motor

(120 x 25)/10 = (120 x 60)/ Pm

Pm = 24

Maximum Power Transfer theorem

The maximum power is transferred when the load resistance RL is equal to internal resistance Rth or the equivalent resistance Rth.

RL = Rth

Under this condition, the same amount of power is dissipated in the internal resistance Rth and hence the efficiency is 50%.

A Maxwell bridge is a modification to a Wheatstone bridge used to measure an unknown inductance (usually of low Q value) in terms of calibrated resistance and inductance or resistance and capacitance.

The balanced condition for Maxwell bridge is given as

Z₁Z₄ = Z₂Z₃

Here Z₁ = Rx + jωLx

Z₂ = 200Ω

Z₃ = 750Ω

Z₄ = R₄ ||(1/ωC₄)

For maximum power to be transferred from a source to a load resistance, the value of load resistance should be equal to the internal resistance of the source.

RL = R = 10Ω

current through the circuit = 10/(10+10) = 0.5 A

power transferred = I²R = 0.25 x 10 = 2.5 W

For a dc shunt motor. field current is practically constant and thus the torque is directly proportional to the armature current. Hence the torque-armature current characteristic is a straight line passing through the origin. However, due to the armature reaction under the loaded conditions of the machine. the flux decreases slightly with the load.
Since flux is practically constant for DC shunt motor. The speed of the DC shunt motor is

N = K (V – IaRa)

Armature current increases as the load on the motor are increased. Thus, the speed of the dc shunt motor will fall slightly with the armature current. As the speed characteristic is only slightly drooping, the dc shunt motor is normally regarded as a constant speed motor.