Solving a 1500 W Heater Short Circuit

[Gogsey]

The problem is that a space heater develops a short circuit when to much current enters the circuit. The power supplied is 1500 W and the max current before short circuit is 15A.

Firstly we have to calculate the resistance of the heater where I used P = I^2 R.

But now we have to find the max reistance of the short circuit using circuit analysis, which we know R of the heater from before but we don't know the total current supplied.

I read somewhere that the resistance of a short circuit is zero, but I may have read this wrong.

Then we have to find the mimimum diameter of the wire(the short circuit) if it s 3mm long. It also givees a temp os 273K, and at this temp the heater wasn't working.

Now I know you can set the derivative equal to zero to find max/min values. The other attempt I tried was to use alpha E = I/A, but after some algebra I get and area on both sides in the denominator, and they cancel, and I'm left with V/R = I.

 

[Delphi51]

Yes, a short circuit usually means practically zero resistance, but of course there will be some resistance - for instance from the finite size of the wires. Knowing the length and gauge of the cord and its conductivity you could calculate that. And then there would be the wires from the power company transformer to the plug in the house . . . and so on. The question just doesn't seem to limit the possibilities like it should.

Could you post the exact wording of the question?

 

[Gogsey]

Sure thing, here it is.

One particularly cold day this past December, your instructor turned on his 1500W space heater at home. Unfortunately the copper wires in the heater's power cable had developed a short circuit. As a result, the circuit breaker, which activates for currents above 15A, tripped.

1). What is the value of the reistamce of the heater(R(heater))?

2). What is the maximum possible value that the short circuit resistance(R(sc)) could have?

3). Assume that the room was at 273K(a good assumption, given that te heater wasn't working), and that te short circuit consisted of a cylindrical strand of copper of length 3mm. What is the minimum diameter of the cylinder?

4). What is the maximum drift velocity of the electrons in the short circuit could have? Do you think they reached this value? If not, what does this tell you about the limits on the diameter and R(sc) that you derived?

 

[Gogsey]

Just posted the reply to put it back to the top of the list, lol.