In a potentiometer arrangement, a cell of emf \(1.25\) V gives a balance point at \(35.0\) cm length of the wire. If the cell is replaced by another cell and the balance point shifts to \(63.0\) cm, then the emf of the second cell is:
1. \(1.27\) V
2. \(2.25\) V
3. \(3.27\) V
4. \(3.25\) V

Figure shows a potentiometer with a cell of 2.0 V and internal resistance 0.40 Ω maintaining a potential drop across the resistor wire AB. A standard cell which maintains a constant emf of 1.02 V (for very moderate currents up to a few mA) gives a balance point at 67.3 cm length of the wire. To ensure very low currents drawn from the standard cell, a very high resistance of 600 kΩ is put in series with it, which is shorted close to the balance point. The standard cell is then replaced by a cell of unknown emf ε and the balance point found similarly, turns out to be at 82.3 cm length of the wire. The value of ε is:

1. 1.33 V
2. 1.50 V
3. 1.24 V
4. 1.07 V

Figure shows a potentiometer circuit for comparison of two resistances. The balance point with a standard resistor R=10.0 Ω is found to be 58.3 cm, while that with the unknown resistance X is 68.5 cm. The value of X is:

1. $12.1\Omega$

2. $12.4 \Omega$

3. $10.3 \Omega$

4. $11.7 \Omega$

The figure shows a 2.0 V potentiometer used for the determination of the internal resistance of a 1.5 V cell. The balance point of the cell in the open circuit is 76.3 cm. When a resistor of 9.5 Ω is used in the external circuit of the cell, the balance point shifts to 64.8 cm length of the potentiometer wire. The internal resistance of the cell is:
    
1. \(1.68~\Omega \)
2. \(0.13~\Omega \)
3. \(0.31~\Omega \)
4. \(1.12~\Omega \)