If the length of potentiometer wire is increased, then the length of the previously obtained balance will

Options

A. Increases
B. Decrease with the increase of temperature
C. Remain unchanged
D. Become two times

Explanation

To solve the question, we need to analyze the relationship between the length of the potentiometer wire and the balance length obtained in a previous experiment. Here’s a step-by-step solution:

### Step 1: Understand the Concept of Potential Gradient
The potential gradient (k) of a potentiometer wire is defined as the change in potential (voltage) per unit length of the wire. Mathematically, it can be expressed as:
\[ k = \frac{V}{L} \]
where \( V \) is the voltage across the wire and \( L \) is the length of the wire.

### Step 2: Analyze the Effect of Increasing Wire Length
If we increase the length of the potentiometer wire (let's say from \( L_1 \) to \( L_2 \)), while keeping the voltage \( V \) constant, the new potential gradient \( k' \) will be:
\[ k' = \frac{V}{L_2} \]
Since \( L_2 > L_1 \), it follows that:
\[ k' < k \]
This means that the potential gradient decreases when the length of the wire is increased.

### Step 3: Relate Potential Gradient to Balance Length
In a potentiometer setup, the balance length (let's denote it as \( l \)) is directly proportional to the potential gradient. If the potential gradient decreases, the balance length will increase for the same potential difference across the wire. This can be expressed as:
\[ l \propto \frac{1}{k} \]
Thus, if \( k \) decreases, \( l \) must increase.

### Step 4: Conclusion
From the analysis above, we can conclude that if the length of the potentiometer wire is increased, the length of the previously obtained balance will increase.

### Final Answer
The length of the previously obtained balance will **increase**.

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