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 and the material (and therefore the resistivity) are the same for both conductors, 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, which has twice the length but the same resistance and material as the first conductor, is twice that of the first conductor.
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