A voltmeter of resistance \(660~\Omega\)$\mathrm{}$ reads the voltage of a very old cell to be \(1.32\) V while a potentiometer reads its voltage to be \(1.44\) V. The internal resistance of the cell is:
1. \(30~\Omega\)$\mathrm{}$ 
2. \(60~\Omega\)
3. \(6~\Omega\)
4. \(0.6~\Omega\)$\mathrm{}$

In the following circuit, the battery \(E_1\) has an emf of \(12\) volts and zero internal resistance while the battery \(E\) has an emf of \(2\) volts. If the galvanometer \(G\) reads zero, then the value of the resistance \(X\) in ohms is:

               
1. \(10\)
2. \(100\)
3. \(500\)
4. \(200\)

The figure below shows currents in a part of the electric circuit. The current \(i\) is:
    
1. \( 1.7 \mathrm{~A} \)
2. \( 3.7 \mathrm{~A} \)
3. \( 1.3 \mathrm{~A} \)
4. \( 1 \mathrm{~A}\)

What is the equivalent resistance between \(A\) and \(B\) in the figure below if \(R= 3~\Omega?\)
                   
1. \(9~\Omega\)
2. \(12~\Omega\)
3. \(15~\Omega\)
4. None of these$$

A torch bulb rated \(4.5\) W, \(1.5\) V is connected as shown in the figure below. The emf of the cell needed to make the bulb glow at full intensity is:

1. \(4.5\) V

2. \(1.5\) V

3. \(2.67\) V

4. \(13.5\) V

The metre bridge shown is in a balanced position with \(\frac{P}{Q} = \frac{l_1}{l_2}\). If we now interchange the position of the galvanometer and the cell, will the bridge work? If yes, what will be the balanced condition?

    
1. Yes, \(\frac{P}{Q}=\frac{l_1-l_2}{l_1+l_2}\)
2. No, no null point
3. Yes, \(\frac{P}{Q}= \frac{l_2}{l_1}\)
4. Yes, \(\frac{P}{Q}= \frac{l_1}{l_2}\)

What is total resistance across terminals \(A\) and \(B\) in the following network?

1. \(R\)
2. \(2R\)
3. \(\frac{3R}{5}\)
4. \(\frac{2R}{3}\)

The Wheatstone bridge shown in the figure below is balanced when the uniform slide wire \(AB\) is divided as shown. Value of the resistance \(X\) is:
        

1. \(3~\Omega\)
2. \(4~\Omega\)
3. \(2~\Omega\)
4. \(7~\Omega\)

The current in a wire varies with time according to the equation \(I=(4+2t),\) where \(I\) is in ampere and \(t\) is in seconds. The quantity of charge which has passed through a cross-section of the wire during the time \(t=2\) s to \(t=6\) s will be: