Question

Which of the following statement is true about resistance?

• A. Resistance of a wire does not depend on its length.
• B. Thicker wires offer more resistance than thinner wires.
• C. Resistance depends on the nature of material.
• D. Resistance of a wire depends on the product of length of the wire and area of the wire.

Hint:

Remember the relationship:
- More length (\(l\)) \(\to\) More resistance.
- More thickness (\(A\)) \(\to\) Less resistance.
- Material type (\(\rho\)) \(\to\) Directly affects resistance.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks to identify the correct physical statement regarding the factors that determine the electrical resistance of a conducting wire.

Step 2: Key Formula or Approach:
The electrical resistance (\(R\)) of a uniform conductor is given by:
\[ R = \rho \frac{l}{A} \]

Step 3: Detailed Explanation:

• Let us evaluate each option:
- Option (A): Incorrect, because \(R \propto l\). Resistance is directly proportional to the length of the wire.
- Option (B): Incorrect. Thicker wires have a larger cross-sectional area (\(A\)). Since \(R \propto \frac{1}{A}\), thicker wires offer less resistance than thinner wires.
- Option (C): Correct. The term \(\rho\) (resistivity) depends entirely on the nature of the material. Different materials have different free electron densities, meaning resistance depends directly on the nature of the material.
- Option (D): Incorrect. Resistance depends on the ratio of length to area (\(l/A\)), not their product (\(l \times A\)).

• Therefore, Option (C) is the only mathematically and physically correct statement.


Step 4: Final Answer:
The true statement is that resistance depends on the nature of the material.