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finlep [7]
3 years ago
14

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.
Physics
1 answer:
mihalych1998 [28]3 years ago
4 0

Answer:

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:

R_{a} =\frac{pL_{a} }{A_{a} } =\frac{p*4*L_{0} }{2L_{0}*L_{0}  } =\frac{2p}{L_{0} }

Where

p = 1.5x10⁻²Ωm

L0 = 5.8 cm = 0.058 m

R_{a} =\frac{2*1.5x10^{-2} }{0.058} =0.517ohm

Resistance for case b:

R_{b} =\frac{pL_{b} }{A_{b} } =\frac{pL_{0}}{2L_{0}4L_{0} } =\frac{p}{8L_{0}} =\frac{1.5x10^{-2} }{8*0.058} =0.032ohm

Resistance for case c:

R_{c} =\frac{pL_{c}}{A_{c} } =\frac{p2L_{0}}{L_{0}4L_{0}} =\frac{p}{2L_{0}} =\frac{1.5x10^{-2} }{2*0.058} =0.129ohm

b) The current is equal to:

Current for case a:

I_{a} =\frac{V}{R_{a} } =\frac{3}{0.517} =5.8A

Current for case b:

I_{b} =\frac{V}{R_{b} } =\frac{3}{0.032} =93.75A

Current for case c:

I_{c} =\frac{V}{R_{c} } =\frac{3}{0.129} =23.2A

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