Question

What happens to resistance if the length of the conductor is increased?

• A. \( \text{Decreases} \)
• B. \( \text{No change} \)
• C. \( \text{Increases} \)
• D. \( \text{Doubles} \)

Hint:

Think of it like a long road. The longer the road (conductor), the more effort (resistance) it takes for a car (electron) to travel from one end to the other. Conversely, a wider road (larger cross-sectional area) makes it easier for traffic, thus decreasing resistance.

Answer 1

The Correct Option is C

To solve this problem, let's analyze how the resistance of a conductor changes when its length is increased.

1. Understanding Resistance in Conductors

The resistance (R) of a conductor is a measure of how much it opposes the flow of electric current. It depends on several factors, including the material's properties and physical dimensions.

2. The Resistance Formula

Resistance is calculated using the formula:

\[ R = \rho \frac{L}{A} \]

where:
- \( \rho \) = resistivity of the material (constant for a given material),
- \( L \) = length of the conductor,
- \( A \) = cross-sectional area of the conductor.

3. Effect of Increasing Length

From the formula, we can see that:

• Resistance is directly proportional to the length (\( L \)) of the conductor.
• If the length increases while keeping the cross-sectional area (\( A \)) constant, the resistance will increase proportionally.

4. Analysis of the Given Options

The question presents four possible outcomes when length increases:

1. Decreases: Incorrect - Resistance increases with length, not decreases.
2. No change: Incorrect - Resistance changes with length.
3. Increases: Correct - Resistance is directly proportional to length.
4. Doubles: Partially correct but misleading - Resistance only doubles if length doubles (not specified in question).

5. Practical Example

If we have a copper wire: - Original length: 1m, Resistance: 1Ω - New length: 2m (double), Resistance: 2Ω (double)

This demonstrates the direct proportional relationship.

6. Why This Relationship Matters

Understanding this principle is crucial for: - Designing electrical circuits - Calculating power losses in transmission lines - Selecting appropriate wire lengths for specific applications

7. Final Answer

When the length of a conductor is increased, its resistance increases proportionally.