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 . The resistance of wire A is _____ .

Correct answer: 0 aligned & R= A = V A^2 & R_ A R_ B = A_ B ^2 ~A_ A ^2 = r_ B ^4 r_ A ^4 & R_ A 2 =[ 4 × 10^ -3 2 × 10^ -3 ]^4 & R_ A =32 . aligned

JEE Main 20244 AprilEvening Shift

JEE Main 2024 · 4 April · Evening Shift · Physics · Current Electricity

Two wires A and B are made up of the same material and have the...

Two wires

A

and

B

are made up of the same material and have the same mass. Wire

A

has radius of

2.0 \mathrm{~mm}

and wire

B

has radius of

4.0 \mathrm{~mm}

. The resistance of wire

B

2 \Omega

. The resistance of wire

A

is _____

\Omega

\begin{aligned} & \because \mathrm{R}=\frac{\rho \ell}{\mathrm{A}}=\frac{\rho \mathrm{V}}{\mathrm{A}^2} \\ & \therefore \frac{\mathrm{R}_{\mathrm{A}}}{\mathrm{R}_{\mathrm{B}}}=\frac{\mathrm{A}_{\mathrm{B}}^2}{\mathrm{~A}_{\mathrm{A}}^2}=\frac{\mathrm{r}_{\mathrm{B}}^4}{\mathrm{r}_{\mathrm{A}}^4} \\ & \Rightarrow \frac{\mathrm{R}_{\mathrm{A}}}{2}=\left[\frac{4 \times 10^{-3}}{2 \times 10^{-3}}\right]^4 \\ & \Rightarrow \mathrm{R}_{\mathrm{A}}=32 \Omega .\end{aligned}