A wire of length L and cross-sectional area A has a resistance of 0.5 Ω. A wire of same length (L) and cross-sectional area 2A, made of the same material will have a resistance of ________.

Key Points

• The resistance $R$ of a wire is given by the formula $R = \rho \frac{L}{A}$ , where $\rho$ is the resistivity of the material, $L$ is the length, and $A$ is the cross-sectional area.
• Given the original wire has resistance $R_1 = 0.5 \Omega$ with length $L$ and area $A$ .
• The new wire has the same length $L$ but double the cross-sectional area $2A$ .
• The resistance of the new wire $R_2$ can be calculated as $R_2 = \rho \frac{L}{2A}$ .
• Since $R_1 = \rho \frac{L}{A} = 0.5 \Omega$ , we can write $R_2 = \frac{R_1}{2} = \frac{0.5}{2} = 0.25 \Omega$ .
• Therefore, the resistance of the new wire is 0.25 Ω.

Additional Information

• The resistance of a conductor depends on the material's resistivity, the length of the conductor, and the cross-sectional area.
• Doubling the cross-sectional area of a wire, while keeping the length and material constant, will halve its resistance.
• This principle is essential in designing electrical circuits to ensure proper resistance and conductance values.