Circuit breakers and fuses are devices that fail when current of a specific thre

Question

Circuit breakers and fuses are devices that fail when current of a specific threshold or more flows through it. They serve to protect devices on the circuit from damage and to prevent fires due to overheated wires. Typically, the threshold currents are chosen so that if there is no resistance except the wire then the breaker/fuse will fail^1. On a 120 V circuit in a home, copper wire that is 12 gauges (2.053 mm diameter) is commonly used with 20 A circuit breakers. How much power is being dissipated by the wires by 20 A through a 120 V circuit? Almost all of this power becomes thermal energy in the wires! How much resistance does the wire provide if 120 V generates 19.9 A through the wire? What length of 12-gauge copper wire would provide the resistance you calculated in part b.? You may need to look up properties of such wire. If you wanted to ensure that your 20 A breakers is tripped when the wire completes the circuit, would you make the length of wire longer or shorter than the length you calculated in part c.? e. Just because it's absurd, how many electrons' movement through the wire is measured as 20 A?

Explanation / Answer

Solution:

Let's consider two case for this given condition

Case 1.

Let x be even and y be odd.

Then by definition x = 2n and y = 2m + 1
for n, m integers.

Now consider xy = (2n)(2m + 1)
= 4nm + 2n
= 2(2nm + n)
= 2k
where k = 2nm + n is an integer.

Therefore by definition the product xy is even.

Case2.

Let x be even and y be 0.

Then by definition x = 2n and y = 0

for n, integers.

Now consider xy = (2n)(0)
= 0

as we know that 0 is even number .

Therefore the product xy is even by definition and

both cases verify the truth of our hypothesis that if x is even or y=0 then xy is even .

Answer

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