Two wires A and B are made up of the same material and have the same mass. Wire A has radius of 2.0 mm and wire B has radius of 4.0 mm. The resistance of wire B is 2 Ω. The resistance of wire A i s ______ Ω.
Physics · Current electricity · electric current ,current density and resistance
JEE Mains 2024 04 Apr Evening Shift

Question

Two wires A and B are made up of the same material and have the same mass. Wire A has radius of 2.0 mm and wire B has radius of 4.0 mm. The resistance of wire B is 2 Ω. The resistance of wire A i s ______ Ω.

Physics · Current electricity · electric current ,current density and resistance

JEE Mains 2024 04 Apr Evening Shift

G1 Physics · Accepted Answer

For the same material and same mass, volume is the same: AL = constant So: L ∝ 1/A Resistance: R = ρL/A Therefore: R ∝ 1/A² Since A ∝ r²: R ∝ 1/r⁴ Hence: R(A)/R(B) = [r(B)/r(A)]⁴ = (4/2)⁴ = 16 Given: R(B) = 2 Ω Therefore: R(A) = 32 Ω