Physics
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A0.2 cm diameter wire must carry a 20-a current. if the maximum power dissipation

A0.2 cm diameter wire must carry a 20-a current. if the maximum power dissipation along the wire is 4w/m, what is the minimum allowable conductivity of the wire in ohm-m? (a) 3.18x10 (b) 3.18x10 () 3.18x10 (d) 3.18x10
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Apple557
Apple557
4,4(73 marks)

The conductivity of the wire is 3.18\times10^{7}\ ohm-m.

Explanation:

Given that,

Diameter = 0.2 cm

Current = 20 A

Power = 4 W/m

We need to calculate the conductivity

We know that,

\sigma = \dfrac{1}{\rho}

Using  formula of resistance

R = \dfrac{\rho l}{A}....(I)

Where,

\rho = resistivity

A = area

l = length

Using formula of power

P = i^2 R

R = \dfrac{P}{i^2}

Put the value of R in equation (I)

\dfrac{P}{i^2}=\dfrac{\rho l}{\pi r^2}

\rho=\dfrac{P\pi r^2}{l\timesi^2}

\sigma=\dfrac{l\times i^2}{P\pi r^2}

Put the all values into the formula

\sigma=\dfrac{1\times(20)^2}{4\times3.14\times(0.1\times10^{-2})^2}

\sigma=3.18\times10^{7}\ ohm-m

Hence, The conductivity of the wire is 3.18\times10^{7}\ ohm-m.

betsylancer8522
betsylancer8522
4,4(81 marks)

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