E.M.F equation of an alternator is given as

E = K_c K_d √2π f Φ N_p

Or E = 4.44 K_c K_d  f Φ N_p    ………….. (since √2π = 4.44)

Where

K_c = Coil span factor

K_d = Distribution factor

Φ = Flux per pole

f = frequency

Np = Turns per phase

E = 4.44 × 0.955 × 0.966 × 50 × 25 × 10^-3 × 240

E = 1228.1 volts

Copper loss is proportional to the square of load current. At half load, load current becomes half as voltage remains same, so the copper loss will become (1/2)² i.e 1/4 times of full load copper loss.

So (Pcu)_{full load} = 600 watts

(Pcu) _{half load} = 600/4 = 150 watts

A sodium vapor lamp is also called the cold-cathode low-pressure lamp which gives high luminous output about three times higher than the other lamp.

For starting discharge through the lamp, it is essential that the striking voltage should be higher than the normal working voltage of the lamp. This high voltage is taken from a high reactance transformer or auto-transformer which has poor voltage regulation. Thus when discharge in the lamp takes place, the lamp current increase due to the decrease in the resistance of the gas in the tube and output voltages of the auto-transformer fall. The lamp then continues to operate normally.

Auto-transformer ratio is given as

I1/I2 = N2/N1

60/I2 = 140/210

I2 = 90A

Current in common Winding Ic

Ic = (N2 – N1)I1/N2

=  60 x (210 – 140)/140

= 30 A

Transformer ratio is given by

N1/N2 = V1/V2

0r N2/N1 = V2/V1

6/1 = V2/200

V2 = 1200 volt per phase

For star connection line voltage is

V_L = √3 x 1200 = 2078.46 V

Why inductor behaves as short circuit for DC voltage?

An inductor has a reactance equivalent XL = 2πfL. Since a DC supply will have frequency = 0, the reactance is 0 and the inductor would be short.

Detail explanation

Imagine a circuit of three elements in series – an input voltage source, inductor, and resistive load. The input source has been producing some constant (DC) voltage; If an inductor is connected with a DC source, it will not act as an inductor but acts like a simple resistor. The current through it will depend on the resistance of the inductor. Now increase the input voltage to a higher value.

The inductor immediately converts the voltage change to an equivalent “antivoltage” and applies it contrary to the input voltage change, the voltage “produced” by the inductor “jumps” with a magnitude equal to the input voltage change. Thus we have two voltage sources (an “original” and “cloned”:) contrary connected in series and neutralizing each other; as a result, the total (effective) voltage and accordingly the current do not change. After that, the current will increase exponentially (1 – e^-t) and reach a constant value. The current will be maximum and the inductor will behave like a short circuit.

The total impedance of the series LCR circuit is given as

Z = R + j (X₁ – X_²)

where X₁ is inductive reactance

and X₂ is capacitive reactance.

At a particular frequency (resonant frequency), we find that X₁=X₂ because the resonance of a series RLC circuit occurs when the inductive and capacitive reactances are equal in magnitude but cancel each other because they are 180 degrees apart in phase. Therefore, the phase angle between voltage and current is zero and the power factor is unity.

Thus, at the resonant frequency, the net reactance is zero because X₁=X₂. The circuit impedance Z becomes minimum and is equal to the resistance R. “Since the impedance is minimum, the current will be maximum”.

For Series RLC circuit if the frequency is greater than the resonance frequency than the circuit behaves as an inductive circuit.

As the given circuit is Wheatstone bridge balance circuit

Therefore according to balanced equation of Wheatstone bridge

Req = 20||40

= (20 x 40)/(20 + 40)

= 40/3Ω

The Thevenin equivalent resistance Rs is viewed from the open terminals A and B is given as. As per the Thevenin theorem, when resistance RL is connected across terminals A and B, the network behaves as a source of voltage Vs and internal resistance RT and this is called Thevenin equivalent circuit.