What is the resistance of the second wire?

Steps to Solve

1. Understand the Relationship of Resistance Resistance ($R$) is defined by the formula $$ R = \rho \frac{L}{A} $$ where $\rho$ is the resistivity of the material, $L$ is the length of the wire, and $A$ is the cross-sectional area.

2. Identify Parameters for the Second Wire For the second wire:

• Length ($L_2$) is twice that of the first wire: $L_2 = 2L_1$
• Cross-sectional area ($A_2$) is twice that of the first wire: $A_2 = 2A_1$

3. Calculate the Resistance of the Second Wire Using the resistance formula for the second wire, we replace $L$ and $A$ with their new values: $$ R_2 = \rho \frac{L_2}{A_2} = \rho \frac{2L_1}{2A_1} $$

4. Simplify the Expression for Resistance The $2$ in the numerator and the $2$ in the denominator cancel out: $$ R_2 = \rho \frac{L_1}{A_1} = R_1 $$ Thus, the resistance of the second wire is equal to the resistance of the first wire.

5. Final Calculation Given that the resistance of the first wire ($R_1$) is $8.0\Omega$, the resistance of the second wire ($R_2$) is also: $$ R_2 = 8.0Ω $$