The conductivity of carbon is about 3*(10^4) S/m. a. What size and shape sample of carbon...

The conductivity of carbon is about 3*(10^4) S/m.

a. What size and shape sample of carbon has this conductance? (Conductance is equal to 1/R).

b. What is the conductance if every dimension of the sample found in (a) is cut in half?

Solutions

Expert Solution

Conductivity is the inverse of resistivity. So, if the condictivity is then the resistivity is

Resistance is given by the equation where is the resistivity, L is the lenght of the sample and A is the cross sectional area of the face, through which the current is flowing.

a)Let the conductance be (since it is only said "this conductance").

Now, the above equation can be rewritten as

where G is the conductance, is the conductivity.

Lets assume, for the sake of calculation, that the cross sectional area is , and that face is a square of side 1m.

then

b) Now, we have a cube of side 1m. if we change the side of the cube to 0.5m (half the value of original), then the cross sectional area becomes

and its length becomes 0.5m.

The new conductance will be given by

genius_generous answered 1 year ago

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