A small town with a demand of 800 kW of electric power at 220 V is situated 15 km away from an electric plant generating power at 440 V. The resistance of the two wirelines carrying power is 0.5 $\Omega$ per km. The town gets power from the line through a 4000-220 V step-down transformer at a sub-station in the town. The line power loss in the form of heat is:

1. 100 kW
2. 500 kW
3. 400 kW
4. 600 kW

At a hydroelectric power plant, the water pressure head is at a height of \(300\) m and the water flow available is \(100\) m³ s^-1. If the turbine generator efficiency is \(60\)%, the electric power available from the plant is:
(Take \(g=9.8\) m s^-2)
1. \(111.3\) MW
2. \(210\) MW
3. \(176.4\) MW
4. \(213.5\) MW

A power transmission line feeds input power at 2300 V to a step-down transformer with its primary windings having 4000 turns. What should be the number of turns in the secondary in order to get output power at 230 V?

1. 200
2. 250
3. 350
4. 400

What is the Q-factor of a series LCR circuit with L = 3.0 H, C = 27µF, and R = 7.4 Ω?

1. 45
2. 55
3. 37
4. 49

A simple electric motor has an armature resistance of $1\mathrm{\Omega }$ and runs from a d.c. source of 12 V. It draws a current of 2 A when unloaded. When a certain load is connected to it, its speed reduces by 10% of its initial value. The current drawn by the loaded motor is

1. 3 A

2. 6 A

3. 2 A

4. 1 A

The time required for a 50 Hz sinusoidal alternating current to change its value from zero to the r.m.s. value will be:

1. $1.5\times {10}^{-2}$ $\mathrm{s}$

2. $2.5\times {10}^{-3}$ $\mathrm{s}$

3. ${10}^{-1}$ $\mathrm{s}$

4. ${10}^{-6}$ $\mathrm{s}$

When 100 volt d.c. is applied across a solenoid, a current of 1.0 A flows in it. When 100 volt a.c. is appliead across the same coil, the current drops to 0.5 A. If the frequency of a.c. source is 50 Hz the impedance and inductance of the solenoid is

1. 200 $\mathrm{\Omega }$ and 0.55 H

2. 100 $\mathrm{\Omega }$ and 0.86 H

3. 200 $\mathrm{\Omega }$ and 1.0 H

4. 100 $\mathrm{\Omega }$ and 0.93 H

In a series RLC circuit, potential differences across R, L and C are 30 V, 60 V and 100 V respectively, as shown in the figure. The emf of the source (in volts) will be:

1. 190

2. 70

3. 50

4. 40

In a series LCR circuit, the phase difference between voltage across L and voltage across C is equal to:

When does the voltage in a series LCR circuit lead the current? (Given that ${\mathrm{\omega }}_0=$resonant angular frequency)

1. $\mathrm{\omega }<{\mathrm{\omega }}_0$

2. $\mathrm{\omega }={\mathrm{\omega }}_0$

3. $\mathrm{\omega }>{\mathrm{\omega }}_0$

4. None of these