A 1.00 km cable having a cross-sectional area of 0.500 cm2 is to be constructed

Question

A 1.00 km cable having a cross-sectional area of 0.500 cm2 is to be constructed out of equal lengths of copper and aluminum. This could be accomplished either by making a 0.500 km cable of each one and welding them together end to end or by making two parallel 1.00 km cables, one of each metal. (See the figure (Figure 1) .) ( Resistivities of copper and aluminum are 1.72×108m, 2.63×108m respectively.) Calculate the resistance of the 1.00 km cable for the connection in parallel. Calculate the resistance of the 1.00 km cable for the connection in parallel.

Explanation / Answer

(a)

formula for resitance

R = L/A

when resistance are connected in series

R = (1+2) (L/2)/A

= (2.63* 10^-8 + 1.7* 10^-8)* (500/0.5* 10^-4) = 0.433

1/Rq = 1/ R1 + 1/R2

1/Req = 1/ 1L/A+ 1/ 2L/A

1/Req = A/ 1L + A/2L

1/Req = A/L ( 1/1+ 1/2)

Req = 1/ A/L ( 1/1+ 1/2)

= 1/0.5 * 10^-4/1000 m ( 1/1.72×108m+ 1/2.63×108m)

=0.207 ohm

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