The resistance and the magnitude of the current depend on the path that the curr

Question

The resistance and the magnitude of the current depend on the path that the current takes. The drawing shows three situations in which the current takes different paths through a piece of material. Each of the rectangular pieces is made from a material whose resistivity is ? = 1.50 x 10-2 ?*m, and the unit of length in the drawing is L0 = 5 cm. Each piece of material is connected to a 3.00-V battery. Find (a) the resistance and (b) the current in each case.

Explanation / Answer

R = rho*L/A

rho/Lo = 0.3

I = V/R

Case 1:

R = rho*(4Lo)/(Lo*2Lo) = 2 rho/Lo = 0.6 ohm

I = 3/0.6 = 5A

Case 2:

R = rho*(Lo)/(4Lo*2Lo) = (1/8)(rho/Lo) = 0.0375 ohm

I = 3/0.037580 A

Case 3:

R = rho*(2Lo)/(Lo*4Lo) = 0.5(rho/Lo) = 0.15 ohm

=> I = 3/0.15 = 20 A

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