Question

A material b has twice the specific resistance of material A. A circular wire made of B has twice the diameter of the wire made of A.for the two wires to have the same resistance, the ratio $l_A:l_B$ of their respective lengths must be.

• A. $0.5\Omega$
• B. $4.44\Omega$
• C. $0.888\Omega$
• D. $1\times {10}^{-2}\Omega$

Answer 1

Answer: (A)

$0.5\Omega$

$R_1=\frac{{\rho }_A{l}_A}{\pi R_A^2}$

$R_2=\frac{{\rho }_B{l}_B}{\pi R_B^2}$

$\frac{l_A}{l_B}=\frac{{\rho }_B{R}_A^2}{{\rho }_A{R}_B^2}=\frac{2{\rho }_A{R}_A^2}{{\rho }_{A}4R_A^2}=0.05$