Question #259949

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?

 


1
Expert's answer
2021-11-03T10:23:18-0400

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


Cost=Rate×P×t,Cost=Rate\times P\times t,Cost=$0.15kWh×60 W×30 days×24 h1 day,Cost=\dfrac{\$0.15}{kWh}\times60\ W\times30\ days\times\dfrac{24\ h}{1\ day},Cost=$0.15kWh×43.2 kWh=$6.48.Cost=\dfrac{\$0.15}{kWh}\times43.2\ kWh=\$6.48.

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


j=IA=Iπr2,j=\dfrac{I}{A}=\dfrac{I}{\pi r^2},j=4 Aπ×(0.08 m)2=200 Am2.j=\dfrac{4\ A}{\pi\times(0.08\ m)^2}=200\ \dfrac{A}{m^2}.

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