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 $B$ is $2 \Omega$. The resistance of wire $A$ is ________ $\Omega$.
Answer (integer)
32
Solution
<p>$$\begin{aligned}
& R=\rho \frac{I}{A}=\rho \frac{V}{A^2} \\
& \text { and } \pi r_1^2 I_1=\pi r_2^2 I_2 \\
& A_1 I_1=A_2 I_2 \\
& \text { So } \frac{R_1}{R_2}=\left(\frac{A_2}{A_1}\right)^2 \\
& \Rightarrow \frac{R}{2}=\left(\frac{r_2}{r_1}\right)^4 \\
& \Rightarrow R=32
\end{aligned}$$</p>
About this question
Subject: Physics · Chapter: Current Electricity · Topic: Ohm's Law and Resistance
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