A battery is connected across a resistance wire of uniform cross-section . If another resistance wire is connected in parallel, then the intensity of electric field in the first wire will

Options

A. be halved
B. be doubled
C. become zero
D. remain unchanged

Explanation

To solve the problem, we need to analyze the situation when a second resistance wire is connected in parallel to the first wire. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Circuit Configuration
We have a battery connected across a resistance wire (let's call it R1) of uniform cross-section. When we connect another resistance wire (R2) in parallel to R1, we need to determine how this affects the electric field in the first wire (R1).

**Hint:** Visualize the circuit with the battery and the two resistors in parallel. This will help you understand the voltage distribution.

### Step 2: Analyze the Electric Field
The intensity of the electric field (E) in a conductor can be expressed as:
\[ E = -\frac{dV}{dx} \]
where \( V \) is the potential difference across the wire and \( x \) is the length of the wire.

**Hint:** Remember that the electric field is related to the potential difference and the length of the conductor.

### Step 3: Consider the Voltage Across the Wires
In a parallel circuit, the voltage across each component is the same. Therefore, when the second wire (R2) is connected in parallel with the first wire (R1), the voltage across R1 remains the same as the voltage supplied by the battery.

**Hint:** Think about how connecting components in parallel affects voltage.

### Step 4: Evaluate the Length of the Wire
The length of the first wire (R1) does not change when R2 is added in parallel. Thus, the distance \( x \) in the equation for electric field remains constant.

**Hint:** The physical dimensions of R1 are unchanged by the addition of R2.

### Step 5: Conclude the Effect on Electric Field
Since both the voltage (V) across R1 and the length (x) of R1 remain unchanged, the electric field \( E \) in the first wire will also remain unchanged.

**Hint:** Consider how changes in voltage or length would affect the electric field.

### Final Answer
The intensity of the electric field in the first wire (R1) will remain unchanged when another resistance wire (R2) is connected in parallel.

### Summary
- The electric field in the first wire remains constant because the voltage across it does not change and its length remains the same.

### Answer: The intensity of electric field in the first wire will remain unchanged.