- A conductor of length 10 cm has a resistance of 10 ohm. Find the resistance of another conductor of the same material and length having the same area of cross-section but twice the diameter of the first conductor. (JEE Main 2013)
Answer:
The resistance of a conductor is given by:
R = ρl/A
where ρ is the resistivity of the material, l is the length, and A is the area of cross-section.
In this case, the resistivity of the material is the same for both conductors, and the length is the same. The only difference is the area of cross-section. The area of cross-section of the second conductor is twice that of the first conductor, so the resistance of the second conductor will be half that of the first conductor:
R2 = 1/2 * R1 = 1/2 * 10 = 5 Ω
Explanation:
The resistance of a conductor is inversely proportional to the area of cross-section. This means that, if the area of cross-section is doubled, the resistance will be halved. In
