Question

An electric cable contains a single copper wire of radius 9 mm. It’s resistance is 5 Ω. This cable is replaced by six insulated copper wires, each of radius 3 mm. The resultant resistance of cable will be

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

Answer 1

Answer: (A)

7.5 Ω

Answer 2

Initially : Resistance of given cable $R = \rho\frac{l}{\pi \times (9 \times 10^{- 3})^{2}}$

….. (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