Question

A rectangular solid made of carbon has sides of lengths 1.0 cm, 2.0 cm, and 4.0 cm resistivity is ρ = 3.5×10−5 ω⋅m . determine the resistance for current that passes through the solid in -"g.com"

Answer 1

Missing part in the text of the question. Found the rest on internet:
"determine the resistance for current that passes through the solid in (a) the x direction (b) the y direction and (c) the z direction"

Solution

The relationship between resistance and resitivity is given by

`R= (\rho L)/(A)`
where R is the resistance

`\rho` is the resistivity of the material (for carbon, as in this problem,
`\rho=3 \cdot 10^(-5) \Omega m`)
L is the length of the conductor
A is its cross-sectional area.

We can solve the 3 parts of the problem by using the same formula, but every time L and A will be different (because they will depend on the direction of the current)

(a) the current is in the x-direction, so the length of the conductor is

`L=1.0 cm=0.01 m`
while the cross sectional area is

`A=(2.0 cm)(4.0 cm)=8.0 cm^2 = 8.0 \cdot 10^(-4)m^2`
So the resistance in this case is

`R= (\rho L)/(A) = ((3 \cdot 10^(-5)\Omega m)(0.01 m))/(8.0 \cdot 10^(-4) m^2) = 3.8 \cdot 10^(-4)\Omega`

(b) the current is in the y-direction, so the length of the conductor is

`L=2.0 cm=0.02 m`
while the cross sectional area is

`A=(1.0 cm)(4.0 cm)=4.0 cm^2 = 4.0 \cdot 10^(-4)m^2`
So the resistance in this case is

`R= (\rho L)/(A) = ((3 \cdot 10^(-5)\Omega m)(0.02 m))/(4.0 \cdot 10^(-4) m^2) = 1.5 \cdot 10^(-3)\Omega`

(c) the current is in the z-direction, so the length of the conductor is

`L=4.0 cm=0.04 m`
while the cross sectional area is

`A=(1.0 cm)(2.0 cm)=2.0 cm^2 = 2.0 \cdot 10^(-4)m^2`
So the resistance in this case is

`R= (\rho L)/(A) = ((3 \cdot 10^(-5)\Omega m)(0.04 m))/(2.0 \cdot 10^(-4) m^2) = 6.0 \cdot 10^(-3)\Omega`