A block of carbon, 1.0 cm by 2.0 cm by 5.0 cm has a resistance of 0.80 Ω between its two smaller faces. What is the resistivity of carbon?
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To find the resistivity (ρ) of carbon, we need to use the formula:
Resistance (R) = (Resistivity ρ) * (Length l / Area A)
Given: R = 0.80 Ω, Length l = 5.0 cm, and the two smaller faces of the carbon block have dimensions 1.0 cm by 2.0 cm.
First, we need to calculate the area of one of the smaller faces:
Area A = length l * width w
Since the dimensions of the face are given as 1.0 cm by 2.0 cm, the area is:
A = 1.0 cm * 2.0 cm = 2.0 cm²
Now, solving the formula for resistivity ρ, we have:
ρ = R * (A / l)
Substituting the given values, we get:
ρ = 0.80 Ω * (2.0 cm² / 5.0 cm)
Let's calculate the resistivity:
ρ = 0.80 Ω * 0.40 cm
ρ = 0.32 Ω·cm
Therefore, the resistivity of carbon is 0.32 Ω·cm.