A cylindrical conductor of length ‘l’ and uniform area of cross-section ‘A’ has resistance ‘R’. What will bethe area of cross-section of another conductor of same material and same resistance but of length ‘2l’.
Question
A cylindrical conductor of length ‘l’ and uniform area of cross-section ‘A’ has resistance ‘R’. What will bethe area of cross-section of another conductor of same material and same resistance but of length ‘2l’.
Solution
The resistance (R) of a conductor is given by the formula:
R = ρl/A
where:
- R is the resistance,
- ρ (rho) is the resistivity of the material,
- l is the length of the conductor, and
- A is the cross-sectional area of the conductor.
Given that the resistance is the same for both conductors, and the length of the second conductor is twice that of the first, we can set up the following equation:
R = ρl/A = ρ(2l)/A'
where A' is the cross-sectional area of the second conductor.
Solving for A', we get:
A' = 2A
So, the cross-sectional area of the second conductor is twice that of the first conductor.
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