If the current in a potentiometer increases, the position of the null point will

Options

A. be obtained at a larger length than the previous one
B. be equal to the previous length
C. be obtained at a smaller length than the previous
D. none of these

Explanation

To solve the question, we need to analyze how the current in a potentiometer affects the position of the null point. The null point is the point at which the potential difference across the potentiometer wire balances the potential difference of the source being measured.

### Step-by-Step Solution:

1. **Understanding the Potentiometer**: A potentiometer is a device used to measure voltage by balancing it against a known voltage. The null point is reached when the potential difference across a certain length of wire equals the voltage of the source.

2. **Potential Gradient**: The potential gradient (E) in a potentiometer is defined as the potential drop per unit length of the wire. Mathematically, it can be expressed as:
\[ E = \frac{V}{L} \]
where \( V \) is the potential difference across the length \( L \) of the wire.

3. **Ohm's Law**: According to Ohm's law, the potential difference \( V \) across the wire can also be expressed as:
\[ V = IR \]
where \( I \) is the current flowing through the wire and \( R \) is the resistance of the wire.

4. **Combining the Equations**: By substituting Ohm's law into the potential gradient equation, we get:
\[ E = \frac{IR}{L} \]
This shows that the potential gradient \( E \) is directly proportional to the current \( I \) and inversely proportional to the length \( L \).

5. **Effect of Increasing Current**: If the current \( I \) increases, the potential gradient \( E \) also increases. Since \( E \) is inversely proportional to \( L \), this means that for a higher potential gradient, the length \( L \) must decrease to maintain the balance.

6. **Conclusion**: Therefore, when the current in the potentiometer increases, the position of the null point will be at a smaller length than the previous one. Thus, the correct answer is that the null point is obtained at a smaller length than the previous one.

### Final Answer:
The position of the null point will be at a smaller length than the previous one.

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