A potentiometer circuit has been set up for finding the internal resistance of a given cell. The main battery, used across the potentiometer wire, has an emf of \(2.0~\text{V}\) and negligible internal resistance. The potentiometer wire itself is \(4~\text{m}\) long. When the resistance, \(R\), connected across the given cell, has values of (i) infinity (ii) \(9.5\), the 'balancing lengths, on the potentiometer wire, are found to be \(3~\text{m}\) and \(2.85~\text{m}\), respectively. The value of the internal resistance of the cell is (in ohm):
1. \(0.25\)
2. \(0.95\)
3. \(0.5\)
4. \(0.75\)

A wire of resistance \(4~\Omega\) is stretched to twice its original length. The resistance of a stretched wire would be:
1. \(4~\Omega\)
2. \(8~\Omega\)
3. \(16~\Omega\)
4. \(2~\Omega\)

In the circuit shown cells, \(A\) and \(B\) have negligible resistance. For \(V_A =12 ~\text{V}\), \(R_1 = 500 ~\Omega \), and $\mathrm{}$\(R = 100 ~\Omega \) the galvanometer \((\text{G}) \) shows no deflection. The value of \(V_B\) is: 
     

1. \(4\) V
2. \(2\) V
3. \(12\) V
4. \(6\) V

If the voltage across a bulb rated \((220~\text{V}\text-100~\text{W})\) drops by \(2.5\%\) of its rated value, the percentage of the rated value by which the power would decrease is:
1. \(20\%\)
2. \(2.5\%\)
3. \(5\%\)
4. \(10\%\)

A ring is made of a wire having a resistance of \(R_0=12~\Omega.\). Find points \(\mathrm{A}\) and \(\mathrm{B}\), as shown in the figure, at which a current-carrying conductor should be connected so that the resistance \(R\) of the subcircuit between these points equals \(\frac{8}{3}~\Omega\)$\mathrm{?}$
      
1. \(\frac{l_1}{l_2} = \frac{5}{8}\)
2. \(\frac{l_1}{l_2} = \frac{1}{3}\)
3. \(\frac{l_1}{l_2} = \frac{3}{8}\)
4. \(\frac{l_1}{l_2} = \frac{1}{2}\)

If power dissipated in the 9 $\mathrm{\Omega }$ resistor in the circuit shown is 36 W, the potential difference across the 2 $\mathrm{\Omega }$ resistor will be:

A current of 2 A flows through a 2 $\mathrm{\Omega }$ resistor when connected across a battery. The same battery supplies a current of 0.5 A when connected across a 9 $\mathrm{\Omega }$ resistor. The internal resistance of the battery is: