A potentiometer consists of a wire of length 4 m and resistance `10Omega`. It is connected to a cell of emf 2V.The potential gradient of the wire is

Options

A. 0.5 V/m
B. 2 V/m
C. 5V/m
D. 10V/m

Answer

To find the potential gradient of the potentiometer wire, we can follow these steps:

### Step 1: Understand the concept of potential gradient
The potential gradient is defined as the potential difference (voltage) per unit length of the wire. It can be mathematically expressed as:

\[ \text{Potential Gradient} = \frac{V}{L} \]

where \( V \) is the potential difference across the wire and \( L \) is the length of the wire.

### Step 2: Identify the given values
From the problem, we have:
- Length of the wire, \( L = 4 \, \text{m} \)
- EMF (potential difference), \( V = 2 \, \text{V} \)

### Step 3: Substitute the values into the formula
Now, we can substitute the values of \( V \) and \( L \) into the formula for potential gradient:

\[ \text{Potential Gradient} = \frac{2 \, \text{V}}{4 \, \text{m}} \]

### Step 4: Calculate the potential gradient
Now, we perform the calculation:

\[ \text{Potential Gradient} = \frac{2}{4} = 0.5 \, \text{V/m} \]

### Conclusion
The potential gradient of the wire is \( 0.5 \, \text{V/m} \).

### Final Answer
The potential gradient of the wire is \( 0.5 \, \text{V/m} \).

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