Question

The resistance of a wire of length 100cm and diameter 0.3m is found to be 30 ohm's.calculate:(1) resistivity (2) conductivity (3) what length of the wire will produce 5 ohm's resistance.

Answer 1

Hi there!

1)

We can use the following equation to solve for resistivity.

`R = (\rho L)/(A)`

R = Resistance (30 Ω)

ρ = Resistivity (? Ωm)

L = Length (100cm = 1 m)
A = Cross-sectional area of wire (r = 0.15m, A = πr², A = 0.0707 m²)

Rearrange the equation to solve for resistivity.

`\rho = (RA)/(L)\\\\\rho = (30 * 0.0707)/(1) = \boxed{2.121 \Omega m}`

2)
The conductivity of a resistor is equivalent to:

`\sigma = (1)/(\rho)`

σ = Conductivity (S/m)

ρ = Resistivity (2.121 Ωm)

Solve:

`\sigma = (1)/(2.121) =\boxed{0.472 (S)/(m)}`

3)
We can use the equation for resistivity to solve. Rearrange the equation for length:

`R = (\rho L)/(A)\\\\L = (AR)/(\rho)\\\\L = (0.0707 * 5)/(2.121) = \boxed{0.167 m}`