Suppose you want to connect your stereo to remote speakers; it requires 20 m len

Question

Suppose you want to connect your stereo to remote speakers; it requires 20 m length of wire per speaker.  Calculate the diameter of copper wire needed to keep the resistance less than 0.10 ? per wire.  If the current to each speaker is 4.0 A, calculate the potential difference (voltage drop) across each wire?  If you were able to stretch uniformly your wire so that it is twice its original length, how does the resistance changes.  Show your calculation.

Suppose you want to connect your stereo to remote speakers; it requires 20 m length of wire per speaker. Calculate the diameter of copper wire needed to keep the resistance less than 0.10 ? per wire. If the current to each speaker is 4.0 A, calculate the potential difference (voltage drop) across each wire? If you were able to stretch uniformly your wire so that it is twice its original length, how does the resistance changes. Show your calculation

Explanation / Answer

V = IR = 4*0.1 = 0.4 Volts

since R = rho L/A

so we know AL = constant

so if you double L you will halve A

so new R = rho (2 L)/(A/2) = 4 R0

so quadruple the original R, so 0.4 ohms

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