The resistance and the magnitude of the current depend on thepath that the curre

Question

The resistance and the magnitude of the current depend on thepath that the current takes. The drawing shows three situations inwhich the current takes different paths through a piece ofmaterial. Each of the rectangular pieces is made from a materialwhose resistivity is = 1.50 x 10-2*m, and the unit of length in the drawing isL0 = 3 cm. Each piece of material is connectedto a 3.00-V battery. Find (a) the resistance and(b) the current in each case.

The resistance and the magnitude of the current depend on thepath that the current takes. The drawing shows three situations inwhich the current takes different paths through a piece ofmaterial. Each of the rectangular pieces is made from a materialwhose resistivity is rho = 1.50 x 10 - 2omega*m, and the unit of length in the drawing isL0 = 3 cm. Each piece of material is connectedto a 3.00 - V battery. Find (a) the resistance and(b) the current in each case

Explanation / Answer

(a)         (a) R =(1.50 x 10-2 *4* 0.03 / 2 * 0.03 * 0.03 )                     = 1        (b)     R = (1.50 x 10-2 *0.03 / 2 * 4 * 0.03 * 0.03 )                     = 0.0625        (c)     R = (1.50 x 10-2 *2*0.03 / 4 * 0.03 * 0.03 )                     = 0.25 (b)         (a) I = V/R = 3 /1 = 3 amp         (b) I = V/R = 3 /0.0625 = 48 amp         (c) I = V/R = 3 /0.25 = 12 amp

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