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.