Question

the resistance of a wire of radius 0.01mm is 10 ohm if the resistivity of the material is 5×10^-7 ohm meter find the length of the wire​

Answer 1

Answer:

Given,

resistance R = 10 ohm

resistivity $\rho$ = $5\:\times\: 10^{-7}\:\:ohm \:\:m$

$\sf \: radius \: \: r = 0.01 \: \: mm \\ \: \: \: \: \: \: \: \: \: \: \: = 0.01 \times {10}^{ - 3} \: \: m \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = 1 \times {10}^{ - 5} \: \: m \\ \sf \: area \: \: A = \pi {r}^{2} \\ \: \: \: \: \: = 3.1416 \times ( {1 \times {10}^{ - 5} })^{2} \\ \: \: \: \: \: \: \: \: = 3.1416 \times {10}^{ - 10} \: \: \: {m}^{2}$

length l = to find

we know that,

$\sf \: R \:=\:\frac{ \rho\:l}{A} \: \\ \sf \implies \: \: l \: = \frac{RA}{ \rho} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{10 \times 3.1416 \times {10}^{ - 10} }{5 \times {10}^{ - 7} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 6.2832 \times {10}^{ - 3} \: \: m \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 6.2832 \: \: mm$