Question

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

• A. 7.5
• B. 90
• C. 45
• D. 270

Answer 1

The correct option is C 45

Resistance $R=\varrho \frac{l}{A}$

where $\varrho =$ resistivity of material

$l=$ lengthy of conductor

$A=$ area of crossection

$R=\varrho \frac{l}{\lambda {\left(9\right)}^2}=5R^1=\varrho \frac{l}{\lambda {\left(3\right)}^2}\times 9=\varrho \frac{l}{\lambda 9}\times 9=5\times 9R^1=45\Omega$

$R^1=$ Resistance of $3$mm radius copper wire.