Question 397: Current Electricity

Question

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

Accepted Answer

$$\begin{aligned}
& R=ho \frac{I}{A}=ho \frac{V}{A^2} \
& 	ext { and } \pi r_1^2 I_1=\pi r_2^2 I_2 \
& A_1 I_1=A_2 I_2 \
& 	ext { So } \frac{R_1}{R_2}=\left(\frac{A_2}{A_1}ight)^2 \
& \Rightarrow \frac{R}{2}=\left(\frac{r_2}{r_1}ight)^4 \
& \Rightarrow R=32
\end{aligned}$$

Current Electricity

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

Choose the correct answer: