Below, a rectangular solid Is made of carbon with sides 2.00 cm, 8.00 cm and 4.0

Question

Below, a rectangular solid Is made of carbon with sides 2.00 cm, 8.00 cm and 4.00 cm parallel to the x, y and z in that order. The resistivity is 3.10 times10-5 ohm-m. Current is allowed to pass in the x direction, -direction or z-direction only. For each possible current direction, you connect wires from a batters across two opposite faces perpendicular to the current. Write neatly and clearly. Determine the resistance K for current that passes along the x direction, y direction. z direction. For the next two parts assume, for each possible current direction, the same voltage difference V is placed across the two opposite faces perpendicular to that current. Which current is thc largest, current in x-direction. current in y-direction or current in z-direction? Explain. (c) Which current is the smallest. current in x-direction, current in y-direction or current in z-direction? Explain.

Explanation / Answer

The formula for finding resistance of a substance is R = L/A where is given as 3.1 X 10-5 m

When the current flows in the x direction, the L = .02 m and the area is (.08)(.04) = 3.2 10-3 m2

Applying R = L/A we have

R = (3.1 X 10-5 m)(.02 m)/3.2 10-3 m2

R = 1.94 X 10-4

In the y direction, L = .04 m and A = (.08)(.02) =  1.6 10-3 m2

R = (3.1 X 10-5 m)(.04 m)/1.6 10-3 m2

R = 7.75 X 10-4

In the z direction, L = .08 m and A = (.04)(.02) = 8 x 10-4 m2

R = (3.1 X 10-5 m)(.08 m)/8.0 10-4 m2

R = 3.1 X 10-3

To determine currents, use the Ohm's Law comparison. Since V = IR, if you apply a constant Voltage. if the resistance increases, the current must decrease. Therefore the side with the largest resistance will have the smallest current, and the side with the smallest resistance will have the largest current

Thus, for part B, the largest current is in the x direction where the resistance is smallest

For part C, the smallest current in in the z direction where the resistance is largest

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