A 10 m long wire of resistance 15 ohm is connectd in series with a battery of emf 2V (no internal resistance) and a resistance of 5 ohm. The potential gradient along the wire is

Options

A. `0.15Vm^(-1)`
B. `0.45Vm^(-1)`
C. `1.5Vm^(-1)`
D. `4.5Vm^(-1)`

Explanation

To find the potential gradient along a wire, we can follow these steps:

### Step 1: Understand the Circuit
We have a circuit consisting of:
- A wire of length \( L = 10 \, \text{m} \) and resistance \( R_{\text{wire}} = 15 \, \Omega \)
- A battery with an emf \( E = 2 \, \text{V} \)
- An additional resistance \( R_{\text{ext}} = 5 \, \Omega \)

### Step 2: Calculate Total Resistance
The total resistance in the circuit can be calculated by adding the resistance of the wire and the external resistance:
\[ R_{\text{total}} = R_{\text{wire}} + R_{\text{ext}} = 15 \, \Omega + 5 \, \Omega = 20 \, \Omega \]

### Step 3: Calculate the Current in the Circuit
Using Ohm's law, the current \( I \) flowing through the circuit can be calculated as:
\[ I = \frac{E}{R_{\text{total}}} = \frac{2 \, \text{V}}{20 \, \Omega} = 0.1 \, \text{A} \]

### Step 4: Calculate the Potential Difference Across the Wire
The potential difference \( V_{\text{wire}} \) across the wire can be found using Ohm's law:
\[ V_{\text{wire}} = I \times R_{\text{wire}} = 0.1 \, \text{A} \times 15 \, \Omega = 1.5 \, \text{V} \]

### Step 5: Calculate the Potential Gradient
The potential gradient \( K \) along the wire is defined as the potential difference across the wire divided by the length of the wire:
\[ K = \frac{V_{\text{wire}}}{L} = \frac{1.5 \, \text{V}}{10 \, \text{m}} = 0.15 \, \text{V/m} \]

### Final Answer
The potential gradient along the wire is \( 0.15 \, \text{V/m} \).

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