A metal wire of specific resistance 64× 10-6Ω cm and length 198 cm has a resistance of 7 Ω . The radius of the wire will be

Question

A metal wire of specific resistance 64× 10-6Ω cm and length 198 cm has a resistance of 7 Ω . The radius of the wire will be (A) 2.4 cm (B) 0.24 cm (C) 0.024 cm (D) 24 cm

Tardigrade Admin · Accepted Answer

Specific resistance ρ=(R A/l) =(R π r2/l) ⇒ r2 =(ρ l/R π) =(64 × 10-6 × 198/7 × 3.14) r =0.024 cm

Q. A metal wire of specific resistance $64 \times 1 0^{- 6} Ω c m$ and length $198 c m$ has a resistance of $7 Ω$ . The radius of the wire will be

2.4 cm

0.24 cm

0.024 cm

24 cm

Specific resistance $ρ = \frac{R A}{l}$
$= \frac{R π r ^{2}}{l}$
$\Rightarrow r^{2} = \frac{ρl}{R π}$
$= \frac{64 \times 1 0 ^{- 6} \times 198}{7 \times 3.14}$
$r = 0.024 c m$

Q. A metal wire of specific resistance 64×10−6Ωcm and length 198cm has a resistance of 7Ω . The radius of the wire will be