Question

Two metal wires have the resistivity 1.62 10^-8 and 4.86 x 10^-8. Compare the resistance of the two wires if wire A is twice as long as wire B and half of its diameter.

Answer 1

Answer:

Hence the resistance of wire A will be 8/3 times the resistance of wire B

Step-by-step explanation:

Let the length of wire A = l

=> the length of wire B = l/2

let the radius of wire A  = r

=> the radius of wire B  = 2r

Area of cross section of wire A,  = πr²

Area of cross section of wire B,  = π(2r)² = 4πr²

we know that resistance of a wire is given by,

R = ρL/A

where ρ = resistivity

Resistance of wire A = (1.62 x 10⁻⁸) x l/πr²

Resistance of wire B = 4.86 x 10⁻⁸ x (l/2)/4πr²

= (4.86/8) x 10⁻⁸ x l/πr²

Hence

Resistance of A/Resistance of B = [(1.62 x 10⁻⁸) x l/πr²]/ [(4.86/8) x 10⁻⁸ x l/πr²]

=> Resistance of A/Resistance of B = 8/3