In an electrical cable there is a single wire of radius 9 mm of copper. Its resistance is 5 Ω Ω . The cable is replaced by 6 different insulated copper wires, the radius of each wire is 3 mm. Now the total resistance of the cable will be
Text Solution
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Initiall: Resistance of given cable
$R = \rho \frac{1}{\pi \times (9 \times 10^{-3})^2}$ ... (i)
Finally: Resistance of each insulated copper wire is
$R' = \rho \frac{l}{\pi \times (3 \times 10^{-3})^2}$ .
Hence equivalent resistance of cable $R_{eq} = \frac{R'}{6} = \frac{1}{6} \times \left( \rho \frac{l}{\pi \times (3 \times 10^{-3})^2} \right)$ ….(ii)
On solving equation (i) and (ii) we get R eq = 7.5 Ω Ω
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