Answer to Question #259949 in Electric Circuits for zuzu

Question

a) How much would it cost to run a 60 W bulb for 1 month if energy costs $0.15 per kWh?

b) Assume the current density is uniform (equal density) across the cross section of a wire with radius r=8 cm. Suppose that the total current flow is I=4A. What is the current density?

 

Answer 1

(a) We can find the cost of the electricity as follows:

$$Cost=Rate\times P\times t,$$ $$Cost=\dfrac{\$0.15}{kWh}\times60\ W\times30\ days\times\dfrac{24\ h}{1\ day},$$ $$Cost=\dfrac{\$0.15}{kWh}\times43.2\ kWh=\$6.48.$$

(b) The current density can be found as follows:

$$j=\dfrac{I}{A}=\dfrac{I}{\pi r^2},$$ $$j=\dfrac{4\ A}{\pi\times(0.08\ m)^2}=200\ \dfrac{A}{m^2}.$$