Electric physics.....

Electricity and Magnetism Level 2

Two wires that are made up of two different materials, whose specific resistances are in the ratio 3:2, length 4:3 and area 5:4. The ratio of their resistance is

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Jasveen Sandral by Jasveen Sandral , 20, India

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1 solution

Tom Engelsman
Jun 21, 2020

Let ρ 1 ρ 2 = 3 2 , L 1 L 2 = 4 3 , A 1 A 2 = 5 4 . \frac{\rho_{1}}{\rho_{2}} = \frac{3}{2}, \frac{L_{1}}{L_{2}} = \frac{4}{3}, \frac{A_{1}}{A_{2}} = \frac{5}{4}. The ratio of resistances computes to:

R 1 R 2 = ρ 1 L 1 A 1 / ρ 2 L 2 A 2 = ρ 1 L 1 A 2 ρ 2 L 2 A 1 = ( 3 2 ) ( 4 3 ) ( 4 5 ) = 8 5 . \frac{R_{1}}{R_{2}} = \frac{\rho_{1}L_{1}}{A_{1}} / \frac{\rho_{2}L_{2}}{A_{2}} = \frac{\rho_{1}L_{1}A_{2}}{\rho_{2}L_{2}A_{1}} = (\frac{3}{2})(\frac{4}{3})(\frac{4}{5}) = \boxed{\frac{8}{5}}.

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