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 the same material whose resistivity is rho = 1.50 x 10^-2 Ω·m, and the unit of length in the drawing is L0 = 5.80 cm. Each piece of material is connected to a 3.00-V battery. Find:

a. the resistance
b. the current in each case.

a) Ra = 0.517 Ω

Rb = 0.032 Ω

Rc = 0.129 Ω

b) Ia = 5.8A

Ib = 93.75A

Ic = 23.2 A

Explanation:

a) The resistance is equal to:

Resistance for case a:

Where

p = 1.5x10⁻²Ωm

L0 = 5.8 cm = 0.058 m

Resistance for case b:

Resistance for case c:

b) The current is equal to:

Current for case a:

Current for case b:

Current for case c:

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total distance/total time

(85 + 82)/(5+3)

167/8

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