Answer to Question #177479 in Physics for Patricia

Question

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?

Answer 1

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

$$R=\rho\dfrac{L}{A}=\rho\dfrac{4L}{\pi d^2},$$ $$R=1.724\cdot10^{-8}\ \Omega\cdot m\dfrac{4\cdot30\ m}{\pi\cdot(2\cdot10^{-3}\ m)^2}=0.165\ \Omega.$$

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

$$P=I^2R,$$ $$I=\sqrt{\dfrac{P}{R}}=\sqrt{\dfrac{2\cdot10^{-4}\ W}{0.165\ \Omega}}=0.035\ A.$$