Question

An electric cable of copper has just one wire of radius 9 mm. Its resistance is 14Ω. If this single copper wire of the cable is replaced by seven identical well insulated copper wires each of radius 3 mm connected in parallel, then the new resistance of the combination will be:

Options

• 9Ω

• 18Ω

• 28Ω

• 126Ω

Answer 1

18Ω

Explanation:

As R = `(rhol)/"A"` ⇒ R_i = 14Ω = `(rhol_0)/(pi"r"_0^2)`

Rf = `(rhol_0)/(pi(r_0/3)^2)`

= 9`(rhol_0)/(pi"r"_0^2)`

= 9R_i

= 9 × 14

= 126Ω

R_eq = `"R"_"f"/7`

= `126/7`

= 18Ω