A potentiometer circuit is set up as shown in the figure below. The potential gradient across the potentiometer wire is k volt/cm. Ammeter present in the circuit reads 1.0 A when the two-way key is switched off. The balance points, when the key between the terminals (i) 1 and 2 (ii) 1 and 3, is plugged in, are found to be at lengths $l_1$ $cm$ and $l_2$ $cm$ respectively. The magnitudes of the resistors R and X in ohm, are then, respectively, equal to: 
   

1. $k(l_2-l_1)$ $and$ $k{l}_2$

2. $k{l}_1$ $and$ $k(l_2-l_1)$

3. $k(l_2-l_1)$ $and$ $k{l}_1$

4. $k{l}_1$ $and$ $k{l}_2$

Given below two statements:

A wire of resistance \(12~ \Omega \text{m}^{-1}\)${\mathrm{}}^{}$ is bent to form a complete circle of radius \(10~\text{cm}\). The resistance between its two diametrically opposite points, \(A\) and \(B\) as shown in the figure, is:
        
1. \(0.6\pi~\Omega\)$$
2. \(3\pi ~\Omega\)$$
3. \(61 \pi~ \Omega\)$$
4. \(6\pi~\Omega\)$$

See the electrical circuit shown in this figure. Which of the following is a correct equation for it?
                                  

A current of \(3~\text{A}\) flows through the \(2~\Omega\) resistor shown in the circuit. The power dissipated in the \(5~\Omega\) resistor is:
    

A cell can be balanced against 100 cm and 110 cm of potentiometer wire, respectively with and without being short-circuited through a resistance of 10 Ω. Its internal resistance is:

1.  1.0 Ω

2.  0.5 Ω

3.  2.0 Ω

4.  zero

The total power dissipated in watts in the circuit shown below is:

Three resistances \(\mathrm P\), \(\mathrm Q\), and \(\mathrm R\), each of \(2~\Omega\) and an unknown resistance \(\mathrm{S}\) form the four arms of a Wheatstone bridge circuit. When the resistance of \(6~\Omega\) is connected in parallel to \(\mathrm{S}\), the bridge gets balanced. What is the value of \(\mathrm{S}\)?
1. \(2~\Omega\)
2. \(3~\Omega\)
3. \(6~\Omega\)
4. \(1~\Omega\)