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 rms value will be:
1. \(1 . 5 \times 10^{- 2}~\text{s}\)

2. \(2 . 5 \times 10^{- 3}~\text{s}\)

3. \(10^{- 1}~\text{s}\)

4. \(10^{- 6}~\text{s}\)

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. \(40\)

A power transmission line feeds input power at \(2300~\text V\) 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 \(230~\text V?\)
1. \(200\)
2. \(250\)
3. \(350\)
4. \(400\)

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 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 \(4000 \text { - }220\) 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