Question

If the length of a linear conductor is doubled and its area of cross section halved, its resistance is

• A. doubled
• B. halved
• C. tripled
• D. quadrupled
• E. unchanged

Hint:

Increasing length increases resistance, and decreasing area also increases resistance. Since both changes act in the same direction, you should expect a significant increase. Doubling length (\(\times 2\)) and halving area (\(\times 2\)) gives a total factor of 4.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The resistance of a conductor is directly proportional to its length and inversely proportional to its cross-sectional area. This relationship depends on the material's resistivity, which remains constant.

Step 2: Key Formula or Approach:
\[ R = \rho \frac{L}{A} \]

Step 3: Detailed Explanation:
Let the initial resistance be \(R = \rho \frac{L}{A}\).
New length \(L' = 2L\)
New area \(A' = \frac{A}{2}\)
The new resistance \(R'\) is:
\[ R' = \rho \frac{L'}{A'} = \rho \frac{2L}{A/2} \]
\[ R' = 4 \left( \rho \frac{L}{A} \right) = 4R \]
The resistance becomes four times the original value, which means it is quadrupled.

Step 4: Final Answer:
The resistance is quadrupled.