When a cell of e.m.f 3.06V is connected, the balance of a potentiometer is 75cm, Calculate the new balance of a cell of e.m.f  2.295V

Analysis

This question tests your understanding of the Principle of a Potentiometer. A potentiometer works on the principle that the potential difference across a length of a uniform wire is directly proportional to its length, provided the current flowing through the wire remains constant.

Concept

The relationship between the electromotive force (e.m.f) of a cell and its corresponding balance length on a potentiometer is given by the formula:

Where:

• $E_1 = 3.06\text{ V}$ (Initial e.m.f)
• $L_1 = 75\text{ cm}$ (Initial balance length)
• $E_2 = 2.295\text{ V}$ (New e.m.f)
• $L_2 = ?$ (New balance length)

Solution

1. Rearrange the formula to solve for $L_2$: $$L_2 = \frac{E_2 \times L_1}{E_1}$$

2. Substitute the given values into the equation: $$L_2 = \frac{2.295 \times 75}{3.06}$$

3. Perform the calculation: • First, multiply the numerator: $2.295 \times 75 = 172.125$ • Next, divide by the denominator: $172.125 \div 3.06 = 56.25$

26cm, which is a result of minor rounding differences in the calculation process, but 56.25cm is the exact mathematical result.)*

Conclusion

The new balance length is 56.25cm, which aligns with option A.

Exam Tip

When dealing with potentiometer problems, always remember that the ratio of the e.m.f to the length is constant ($E/L = k$). If the e.m.f decreases, your balance length must also decrease. If you calculate a value larger than your initial length when the e.m.f has dropped, you know you've made a calculation error!