Question

The electrical cable of copper has just one wire of radius $9\, mm$ its resistance is $10\,\Omega$ . This single copper wire is replaced by $3$ different well insulated copper wires each of radius $3\, mm$. The total resistance of the cable will now be equal to :

• A. $90\,\Omega $
• B. $45\, \Omega $
• C. $30\,\Omega $
• D. $15\, \Omega $

Answer 1

Answer: (C)

Resistance of the wire $R \propto \frac{1}{r^{2}(\text { radius })}$ Radius of new wire is $\frac{1}{3} r d$ of the initial wire.
its resistance $R=10(3)^{2}=10 \times 9=90\, \Omega$
Now total resistance of all the $3$ wires in parallel
$=\frac{90}{3}=30\, \Omega$