Resistivity measurements on the leaves of corn plants are a good way to assess stress and overall health. The leaf of a corn plant has a resistance of 2.1 M Ohm measured between two electrodes placed 20cm apart along the leaf. The leaf has a width of 2.8 cm and is 0.20 mm thick.
What is the resistivity of the leaf tissue(Value and Unit)?
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Look for the equation that relates resistance (R) to resistivity.
The unit of resistivity is usually ohm-centimeters
To calculate the resistivity of the leaf tissue, we can use Ohm's law and the formula for the resistance of a cylindrical conductor. The formula for the resistance of a cylindrical conductor is:
R = (ρ * L) / A
Where:
R is the resistance
ρ (rho) is the resistivity
L is the length of the conductor
A is the cross-sectional area of the conductor
In this case, the electrodes are placed 20 cm apart along the leaf, so the length of the conductor (L) is 20 cm. The leaf has a width of 2.8 cm, so we can take this as the cross-sectional area (A) of the leaf.
To convert mm to cm, we divide by 10:
Thickness in cm = 0.20 mm / 10 = 0.02 cm
Now we can calculate the cross-sectional area (A) of the leaf:
A = width * thickness = 2.8 cm * 0.02 cm = 0.056 cm²
We know the resistance (R) is 2.1 M Ohm, which we need to convert to Ohm:
Resistance in Ohm = 2.1 M Ohm * 10^6 = 2.1 * 10^6 Ohm
Now we can rearrange the formula for resistance to solve for the resistivity (ρ):
ρ = (R * A) / L
Plugging in the values:
ρ = (2.1 * 10^6 Ohm * 0.056 cm²) / 20 cm
Calculating this gives us:
ρ ≈ 5.88 * 10^3 Ohm * cm
Therefore, the resistivity of the leaf tissue is approximately 5.88 * 10^3 Ohm * cm.