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.
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
i = σ * A/L = 100 *A/L
i is 10 amps max
10 > 100 A/L
A/L < 0.1
length = 2 then area = 30
A/L = 30/2 = 12, smoke rises from ammeter
length = 30, then area = 2
A/L = 2/30 = 1/15 Caramba ! less than 10 amp
posted by Damon
Thanks for answering this question. Which one is our direction? Direction 1 which is lateral direction or direction 2 which is perpendicular direction.posted by wazowski
I can not see your drawing.
The current should run parallel to the 30 cm length to maximize resistance and minimize current.posted by Anonymous