Copper wire is often used for the construction of practical electric circuits, f

Question

Copper wire is often used for the construction of practical electric circuits, for example, for home wiring, because it has a low resistance to the flow of electricity. More precisely, copper wire has a resistivity rho of about 1.7 times 10^8 ohm-meters. The way that you calculate the actual resistance R of a piece of copper wire of length l and cross-sectional area A is by the equation R = rho l/A. For example, a piece of wire with the length of one centimeter and a cross-sectional area of one square millimeter would have a resistance of about (1.7 times 10^-8)(1 times 10^-2)/(1 times 10^-3)^2 = 1.7 times 10^-4 Ohms. How does this resistance compare to the resistances of the resistors we were using in the lab? How much current could you theoretically get to flow through this piece of wire using one of the 1.5-volt AA batteries we used in the lab? Do you think that you could really get this much current flow? If not, what can you conclude about Ohm's law? Just for fun, compare this current to the amount of current used in an electric chair. On this basis, is it dangerous to play around with AA batteries? Why or why not? Silver is an even better conductor than copper, with a resistivity of about 1.6 times 10^8 ohm-meters. A 100-ounce bar of pure silver has a cross-sectional area of about 20 square centimeters, and a length of about 15 centimeters. How much current could you theoretically get to flow through this bar with a 1.5 volt battery? Compare this to the current delivered by a lightning bolt. Could you generate lightning bolts if you could afford a 100-ounce bar of silver? Why or why not?

Explanation / Answer

a) You must be knowing about the resistance value you have been using in lab but it should be larger than the theoretical values calculated.

b) Using Ohm's law

V = IR

I = V/R = 1.5/1.7*10-4 = 8823.53A

Its difficult to get such huge values of current

Ohm law is valid under certain physical conditions also we generally dont use the wire dimensions given so resistance will be way larger

c) current used in electric chair will be really small compared to this

It is not dangerous playing around a AA battery, but ensure that you don't use the wire with such low resistance.

d) Calculating

R = 1.6*10-8*0.15/20*10-4 = 1.2*10-6 ohms

I = 1.5/1.2*10-6 = 1.25*106 A

Which is very much comparable to current in a lightning bolt

It will be really difficult because of heat energy produced to control it.

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