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. \(10^{- 6}~\text{s}\)

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

An AC voltage source is connected to a series \(LCR\) circuit. When \(L\) is removed from the circuit, the phase difference between current and voltage is \(\dfrac{\pi}{3}\). If \(C\) is instead removed from the circuit, the phase difference is again \(\dfrac{\pi}{3}\) between current and voltage. The power factor of the circuit is:
1. \(0.5\)
2. \(1.0\)
3. \(-1.0\)
4. zero

A \(40~\mu\text F\) capacitor is connected to a \(200~\text V,\)  \(50~\text{Hz}\) AC supply. The RMS value of the current in the circuit is, nearly:
1. \(2.05~\text A\)
2. \(2.5~\text A\)
3. \(25.1~\text A\)
4. \(1.7~\text A\)

A light bulb and an inductor coil are connected to an AC source through a key as shown in the figure below. The key is closed and after some time an iron rod is inserted into the interior of the inductor. The glow of the light bulb:

A direct current of \(5~ A\) is superimposed on an alternating current \(I=10sin ~\omega t\) flowing through a wire. The effective value of the resulting current will be:

An AC ammeter is used to measure the current in a circuit. When a given direct current passes through the circuit, the AC ammeter reads \(6~\text A.\) When another alternating current passes through the circuit, the AC ammeter reads \(8~\text A.\) Then the reading of this ammeter if DC and AC flow through the circuit simultaneously is:
1. \(10 \sqrt{2}~\text A\) 
2. \(14~\text A\) 
3. \(10~\text A\) 
4. \(15~\text A\)