Question

question no. 268

Q268. An electrical cable of copper has just one wire of radius 9 mm. Its resistance is 5 ohm. The single copper wire of the cable is replaced by 6 different well insulated copper wires each of radius 3 mm. The total resistance of the cable will now be equal to

(A) 7.5 Ω (B) 45Ω

(C) 90 Ω (D) 270 Ω
(C.P.M.T. 1988)

Answer 1

Dear student
$$\begin{gathered} Resis\tan ceof\sin glewire \\ R=\frac{\rho l}{A}=\frac{\rho l}{\pi \times 9^2} \\ 5=\frac{\rho l}{\pi \times 9^2}.....1 \\ \frac{\rho l}{\pi }=5\times 9^2 \\ Nowwhenthiswireisreplacedbysixwiresthanthesewiresareconnectedinparallel \\ {R}_{eqv}=\frac{R_o}{6}=\frac{\rho l}{6\times \pi \times 3^2}=\frac{\rho l}{6\times \pi \times 3^2} \\ replacing\frac{\rho l}{\pi }fromeqn1 \\ R=\frac{5\times 9^2}{6\times 9}=\frac{9\times 5}{6}=\frac{3\times 5}{2}=7.5\Omega \\ Regards \end{gathered}$$