Question

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

• A. 7.5 Ω
• B. 45 Ω
• C. 90 Ω
• D. 270 Ω

Answer 1

Answer: (A)

7.5 Ω

Answer 2

R ∝ $\frac{1}{r^{2}}$

Q Radius 9 mm → 3 mm

⇒ Resistance 5Ω → 45Ω

Result of six parallel wires = $\frac{45}{6}$ = 7.5 Ω