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 is ________ Ω. Numerical answer type. Work it out, then open the answer.

Answer: 32. Same material and mass, so same volume V = lA; then R = ρ l/A = ρ V/A² ∝ 1/r⁴. RA/RB = (rB/rA)⁴ = (4/2)⁴ = 16 RA = 16×2 = 32 Ω.

Two wires A and B are made up of the same material and have the same… | JEE Main 2024 (4 Apr, Shift 2)

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Ohm's Law, Resistivity & Temperature

Two wires $A$ and $B$ are made up of the same material and have the same mass. Wire $A$ has radius of $2.0\text{ mm}$ and wire $B$ has radius of $4.0\text{ mm}$ . The resistance of wire $B$ is $2\ \Omega$ . The resistance of wire $A$ is ________ $\Omega$ .

Numerical answer type. Work it out, then open the answer.

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Answer: 32

Same material and mass, so same volume $V = lA$ ; then $R = \rho l/A = \rho V/A^2 \propto 1/r^4$ .
$R_A/R_B = (r_B/r_A)^4 = (4/2)^4 = 16$
$R_A = 16\times2 = 32\ \Omega$ .

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