Answer to Question #177479 in Physics for Patricia

Question #177479

3. A copper wire (ρ=1.724 x 10-8 Ωm) has a length of 30 m and a diameter of 2 mm. (a) If the power on the wire is 2 x 10-4 W, what is the current flowing on the wire? (b) How much current is required?


1
Expert's answer
2021-04-01T18:33:48-0400

(a) Let's first find the resistance of the wire:


R=ρLA=ρ4Lπd2,R=\rho\dfrac{L}{A}=\rho\dfrac{4L}{\pi d^2},R=1.724108 Ωm430 mπ(2103 m)2=0.165 Ω.R=1.724\cdot10^{-8}\ \Omega\cdot m\dfrac{4\cdot30\ m}{\pi\cdot(2\cdot10^{-3}\ m)^2}=0.165\ \Omega.

Finally, we can find the current flowing on the wire:


P=I2R,P=I^2R,I=PR=2104 W0.165 Ω=0.035 A.I=\sqrt{\dfrac{P}{R}}=\sqrt{\dfrac{2\cdot10^{-4}\ W}{0.165\ \Omega}}=0.035\ A.

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