An electric cable contains a single copper wire of radius 9 mm. It’s resistance is 5 ohm. This cable is replaced by six insulated copper wires, each of radius 3 mm. What will be the resultant resistance of cable?
Show <=Solution
Solution :
Initially : Resistance of given cable
\[R=\rho \frac{l}{\pi (9\times 10^{-3})^{2}}\ \cdot \cdot \cdot \cdot (1)\]
Finally : Resistance of each insulated copper wire is
\[R'=\rho \frac{l}{\pi (3\times 10^{-3})^{2}}\ \cdot \cdot \cdot \cdot (2)\]
Hence equivalent resistance of cable,
\[R_{eq}=\frac{R'}{6}=\frac{1}{6}\left [ \rho \frac{l}{\pi (3\times 10^{-3})^{2}}\right ]\ \cdot \cdot \cdot \cdot (3)\]
On solving equation (1) and (3) we get $R_{eq}=7.5 \ ohm$
