A resistance of 2 Ω is to be made from a copper wire (specific resistance 1.7 × 10-8 Ω m ) using a wire of length 50 cm . The radius of the wire is

Question

A resistance of 2 Ω is to be made from a copper wire (specific resistance 1.7 × 10-8 Ω m ) using a wire of length 50 cm . The radius of the wire is (A) 0.0116 mm (B) 0.0367 mm (C) 0.116 mm (D) 0.367 mm

Tardigrade Admin · Accepted Answer

Resistance of a wire, R=(ρ l/A) or A=(ρ l/R) or π r2=(ρ l/R) or r=((ρ l/π R))1 / 2 Substituting the given values, we get r=((1.7 × 10-8 × 0.5/2 × 3.14))1 / 2 =0.367 × 10-4 m=0.0367 mm

Q. A resistance of $2Ω$ is to be made from a copper wire (specific resistance $1.7 \times 1 0^{- 8} Ω m$ ) using a wire of length $50 c m .$ The radius of the wire is

0.0116 mm

0.0367 mm

0.116 mm

0.367 mm

Resistance of a wire, $R = \frac{ρl}{A}$
or $A = \frac{ρl}{R}$ or $π r^{2} = \frac{ρl}{R}$
or $r = (\frac{ρl}{π R})^{1/2}$
Substituting the given values, we get
$r = (\frac{1.7 \times 1 0 ^{- 8} \times 0.5}{2 \times 3.14})^{1/2}$
$= 0.367 \times 1 0^{- 4} m = 0.0367 mm$

Q. A resistance of 2Ω is to be made from a copper wire (specific resistance 1.7×10−8Ωm ) using a wire of length 50cm. The radius of the wire is