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  • Two conductors are made of the same material and have the same length. Conductor A is a solid wire of diameter 1mm. Conductor B is a hollow tube of outer diameter 2mm and inner diameter 1mm. Find the ratio of resistance R_A to R_B.

 Two conductors are made of the same material and have the same length. Conductor A is a solid wire of diameter 1mm. Conductor B is a hollow tube of outer diameter 2mm and inner diameter 1mm. Find the ratio of resistance R_A to R_B.

Answers (1)

Resistance(R)=\rho\frac{L}{A}

R_A=\rho _A\left (\frac{L_A}{A_A} \right ) and R_B=\rho _B\left (\frac{L_B}{A_B} \right )

\rho _A=\rho _B \ and \ L_A=L_B

\frac{R_A}{R_B}=\frac{A_B}{A_A}=\frac{\pi r_A^2}{\pi (r_{out}^2-r_{in}^2)}=\frac{1^2-\left (\frac{1}{2} \right )^{2}}{\left ( \frac{1}{2} \right )^{2}}=\frac{\frac{3}{4}}{\frac{1}{4}}=3

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