The resistance of the ohm is very approximately that of a column of mercury 1.06 m long and of uniform cross-section of one hundred of a cm^2. Find the resistivity of mercury.(show work)
To find the resistivity of mercury, we need to use the formula:
Resistance (R) = Resistivity (ρ) * Length (L) / Cross-sectional Area (A)
Given that the resistance of the ohm is approximately equal to that of a column of mercury, we can write:
R = ρ * L / A
We know the length L is 1.06 m and the cross-sectional area A is 100 cm^2. However, we need to convert the area to square meters first, as the resistivity is usually expressed in terms of ohm-meters.
1 cm^2 = (1/100)^2 m^2 = 0.0001 m^2
Now, substitute the known values into the formula:
R = ρ * (1.06 m) / (0.0001 m^2)
To solve for the resistivity ρ, divide both sides of the equation by (1.06 m) / (0.0001 m^2):
ρ = R / ((1.06 m) / (0.0001 m^2))
Now insert the value for the resistance of the ohm, which is 1 ohm:
ρ = 1 ohm / ((1.06 m) / (0.0001 m^2))
Calculate the result:
ρ = 0.000094 ohm-meters
Therefore, the resistivity of mercury is approximately 0.000094 ohm-meters.