In potentiometer experiment, null point isobtained at a particular point for a cell on potentiometer wire x cm long. If the lengthof the potentiometer wire is increasedwithout changing the cell, the balancing length will (Driving source is not changed)

Options

A. (a)increase
B. (b)decreases
C. (c)not change
D. (d)become zero

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Understand the Potentiometer Principle
The potentiometer is an instrument used to measure the potential difference (voltage) of a cell by balancing it against a known voltage. The balancing length (L) on the potentiometer wire is directly proportional to the voltage of the cell being measured.

### Step 2: Define Initial Conditions
Let:
- \( L_1 \) = initial length of the potentiometer wire
- \( l_1 \) = initial balancing length for the cell
- \( E \) = electromotive force (emf) of the cell
- \( V \) = potential difference across the potentiometer wire

From the potentiometer principle, we have the relation:
\[ \frac{E}{V} = \frac{l_1}{L_1} \]
This equation indicates that the balancing length \( l_1 \) is proportional to the emf \( E \) of the cell and inversely proportional to the total length of the potentiometer wire \( L_1 \).

### Step 3: Increase the Length of the Potentiometer Wire
Now, if the length of the potentiometer wire is increased to \( L_2 \) (where \( L_2 > L_1 \)), we need to find the new balancing length \( l_2 \).

Using the same principle, we can write:
\[ \frac{E}{V} = \frac{l_2}{L_2} \]

### Step 4: Establish the Relationship Between Balancing Lengths
From the two equations, we can express \( l_2 \) in terms of \( l_1 \):
\[ l_1 = \frac{E \cdot L_1}{V} \quad \text{(1)} \]
\[ l_2 = \frac{E \cdot L_2}{V} \quad \text{(2)} \]

### Step 5: Compare the Balancing Lengths
Since \( L_2 > L_1 \), we can substitute the expression for \( l_1 \) into the equation for \( l_2 \):
\[ l_2 = l_1 \cdot \frac{L_2}{L_1} \]

### Step 6: Conclusion
Since \( \frac{L_2}{L_1} > 1 \) (because \( L_2 \) is greater than \( L_1 \)), it follows that:
\[ l_2 > l_1 \]
Thus, the balancing length will increase when the length of the potentiometer wire is increased.

### Final Answer
The balancing length will **increase**.

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