Question:
Two wires of the same material have lengths in the ratio \(1 : 2\) and radii in the ratio \(1 : 2\). The ratio of their specific resistances will be:
Two wires of the same material have lengths in the ratio \(1 : 2\) and radii in the ratio \(1 : 2\). The ratio of their specific resistances will be:
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Do not confuse resistance (\(R\)) with resistivity (\(\rho\)). Resistance depends on dimensions (\(R = \rho \frac{l}{A}\)), but resistivity (\(\rho\)) is a constant for a given material at a constant temperature.
Updated On: Jun 15, 2026
- \(1 : 2\)
- \(2 : 1\)
- \(1 : 1\)
- \(1 : 4\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Question:
The question asks for the ratio of the specific resistances (resistivities) of two wires made of the same material but having different lengths and radii.
Step 3: Detailed Explanation:
Specific resistance, commonly known as resistivity (\(\rho\)), is an intrinsic physical property of a material.
It dictates how strongly a given material opposes the flow of electric current.
Resistivity depends exclusively on the nature of the material (e.g., copper, aluminum) and its temperature. It does not depend on the physical dimensions of the object, such as its length, area of cross-section, or radius.
Since it is explicitly stated that both wires are made of the
same material, their resistivities will be identical regardless of any differences in their lengths or radii.
Therefore, the ratio of their specific resistances is:
\[ \rho_1 : \rho_2 = 1 : 1 \]
Step 4: Final Answer:
The correct choice is (C).
The question asks for the ratio of the specific resistances (resistivities) of two wires made of the same material but having different lengths and radii.
Step 3: Detailed Explanation:
Specific resistance, commonly known as resistivity (\(\rho\)), is an intrinsic physical property of a material.
It dictates how strongly a given material opposes the flow of electric current.
Resistivity depends exclusively on the nature of the material (e.g., copper, aluminum) and its temperature. It does not depend on the physical dimensions of the object, such as its length, area of cross-section, or radius.
Since it is explicitly stated that both wires are made of the
same material, their resistivities will be identical regardless of any differences in their lengths or radii.
Therefore, the ratio of their specific resistances is:
\[ \rho_1 : \rho_2 = 1 : 1 \]
Step 4: Final Answer:
The correct choice is (C).
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