The electrical cable of copper has just one wire of radius 9 mm its resistance is 10 Ω . 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 :

Question

The electrical cable of copper has just one wire of radius 9 mm its resistance is 10 Ω . 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 Ω  (B) 45 Ω  (C) 30 Ω  (D) 15 Ω

Tardigrade Admin · Accepted Answer

Resistance of the wire R propto (1/r2( text radius )) Radius of new wire is (1/3) r d of the initial wire. its resistance R=10(3)2=10 × 9=90 Ω Now total resistance of all the 3 wires in parallel =(90/3)=30 Ω

Q. The electrical cable of copper has just one wire of radius $9 mm$ its resistance is $10 Ω$ . 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 :

$90 Ω$

$45 Ω$

$30 Ω$

$15 Ω$

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

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

90Ω

45Ω

30Ω

15Ω