We know from literature that a certain material “A” exhibits an electrical conductivity of σ=100 S/cm at room temperature. However, we would like to confirm this value by performing electrical conductivity measurements in our labs. To perform these experiments we obtain a sample that has a thickness of 2 cm, a width of 1 cm and a length of 30 cm, as shown in the figure below. Keeping in mind that our measuring device can apply a voltage of 1 V only and can measure a maximum current of 10 amperes, determine in which direction – lateral (direction 1) or perpendicular (direction 2) the measurement must be performed to remain in the range of the capabilities of our measuring device? Show your work and reasoning.

Question

We know from literature that a certain material “A” exhibits an electrical conductivity of σ=100 S/cm at room temperature. However, we would like to confirm this value by performing electrical conductivity measurements in our labs. To perform these experiments we obtain a sample that has a thickness of 2 cm, a width of 1 cm and a length of 30 cm, as shown in the figure below. Keeping in mind that our measuring device can apply a voltage of 1 V only and can measure a maximum current of 10 amperes, determine in which direction – lateral (direction 1) or perpendicular (direction 2) the measurement must be performed to remain in the range of the capabilities of our measuring device? Show your work and reasoning.

Answer 1

current density = σ * E

current i = σ * E * area of cross section
here E = 1 volt / L where L is length in direction of current
so
i = σ * A/L = 100 *A/L
i is 10 amps max
so
10 > 100 A/L
A/L < 0.1
try
length = 2 then area = 30
A/L = 30/2 = 12, smoke rises from ammeter
try
length = 30, then area = 2
A/L = 2/30 = 1/15 Caramba ! less than 10 amp

Answer 2

Thanks for answering this question. Which one is our direction? Direction 1 which is lateral direction or direction 2 which is perpendicular direction.

Answer 3

I can not see your drawing.

The current should run parallel to the 30 cm length to maximize resistance and minimize current.

Answer 4

To determine whether the measurement should be performed in the lateral direction (direction 1) or perpendicular direction (direction 2), we need to calculate the expected current using the given electrical conductivity.

First, let's calculate the cross-sectional area of the sample. The cross-sectional area (A) of a rectangle is given by multiplying the width (w) by the thickness (t):

A = w * t = 1 cm * 2 cm = 2 cm^2

Now, let's calculate the resistance (R) of the sample using the formula:

R = (length / (A * σ)

Substituting the given values, we have:

R = (30 cm) / (2 cm^2 * 100 S/cm) = 0.15 Ω

Next, let's determine the expected current (I) using Ohm's law:

I = V / R

Substituting the voltage (V) of 1 V and the resistance (R), we have:

I = 1 V / 0.15 Ω ≈ 6.67 A

Since the maximum current that our measuring device can measure is 10 A, the expected current of approximately 6.67 A falls within this range.

Therefore, we can conclude that the measurement should be performed in the lateral direction (direction 1) based on the given dimensions and the capabilities of our measuring device.