Maximun power delivered to a resistor

[tadm123]

Homework Statement

Find the maximun possible power delivered to the resistor. Given current through a power line. And the length of the loop that will receive the induced emf.

Homework Equations

B= uo*I/2pi*ρ
Vemf= -d/dt ∫B*dS

The Attempt at a Solution

Here's my attempted solution:

I just need to know if the answer is correct.

Thanks a lot guys.

 

[rude man]

Your emf calculation is not right. You have assumed the B field is everywhere the same inside the loop which it isn't.

You also badly miscalculated the resistance of the copper wire. The area is that of the wire's cross-section, not that of the loop!

 

[tadm123]

Probably a stupid question, but how do I know the cross section area of wire if I'm not given the radius of the wire?

 

[rude man]

Probably a stupid question, but how do I know the cross section area of wire if I'm not given the radius of the wire?

It's not a stupid question it's a very good question.

You somehow need to compute the resistance of the entire loop and can do that if you're given (1) Cu resistivity, (2) length of loop (check) and (3) cross-sectional area of wire (not provided).

 

[tadm123]

Well I'm not very knowledgeable in wires and electronics. But all I was given in the problem was that it is a "#6 wire"

You know what does that mean? Is that some type of wire nowadays already manufactured with it's own specifications ?

 

[rude man]

Well I'm not very knowledgeable in wires and electronics. But all I was given in the problem was that it is a "#6 wire"

You know what does that mean? Is that some type of wire nowadays already manufactured with it's own specifications ?

That means AWG ("American Wire Gauge") #6 gauge wire. You can look up its resistance per foot or whatever on the Web.

 

[tadm123]

I see, thanks a lot.