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  lying on the x, y and x axes in that order. The resistivity is ? = 3.10x10-5 ohm-m.  Current is allowed to pass in the x direction,  y-direction or  z-direction only.  For each possible current direction, you connect wires from a battery  across the two opposite faces perpendicular  to the current.

Determine the resistance R for  current that passes along the  

(a) x direction,

(b) y direction,

(c) 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.

(d) Which current is the largest,   current in x-direction, current in y-direction or current in z-direction? Explain.
(e) Which current is the smallest ,  current in x-direction, current in y-direction or current in z-direction? Explain.

Below, a rectangular solid is made of carbon with sides 2.00 cm, 8.00 cm and 4.00 cm lying on the x, y and x axes in that order. The resistivity is ? = 3.10x10 - 5 ohm - m. Current is allowed to pass in the x direction, y - direction or z - direction only. For each possible current direction, you connect wires from a battery across the two opposite faces perpendicular to the current. Determine the resistance R 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 the largest, current in x - direction, current in y - direction or current in z - direction? Explain. Which current is the smallest , current in x - direction, current in y - direction or current in z - direction? Explain

Explanation / Answer

The total resistance of the block is R = ?*L/A, where L is the length in the direction of the current, and A the cross-sectional area perpendicular to the current.

For the illustration you have,

L = L1
A = L2*L3

so

R = ?*L1/(L2*L3)

Rx = 3.1*10^-5 * 4/16 = 7.75 micro ohm

Ry = 3.1*10^-5 * 8/8 = 31 micro ohm

Rz = 3.1*10^-5 * 2/32 = 1.9375 micro ohm

current in Rz is largest bcoz of low resistance,

current in Ry is smallest bcoz of high resistance,

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