Question

A wire 1m long and 0.31mm in diameter has a resistance of 4.2Ω.Calculate the resistance of another wire of the same material whose length is 1.5m and diameter 0.155mm.​

Answer 1

Use this general formula: R = ρ L / A

L= 1 m

D= 0.031 m, r = 0.0155 m

R = 4.2Ω

ρ = RA / L

$\frac{4.2 \times \pi \times {0.0155}^{2} }{1}$

$= 4.2 \times \pi \times {0.0155}^{2}$

l = 1.5 m

d = 0.0155 m, r = 0.0775 m

ρ = $4.2 \times \pi \times {0.0155}^{2}$

sub in R = ρ L / A

$R = \frac{4.2 \times \pi \times {0.0155}^{2} \times 1.5}{\pi \times {0.0775}^{2} }$

Resistance = 25.2Ω