Answer 1:
Heat given off by a circuit is a form of
energy transfer. In a circuit, the energy
of flowing electrons is being converted into
thermal energy. This transfer of energy
occurs over a period of time and can be described
by a rate of energy transfer. Physicists refer to
"power" as the rate of energy transfer over
time. Now the equation for power of a circuit is:
P = R*I^{2}.
That is, the power (P) is equal to the
resistance (R) of a circuit time the current (I)
squared. This is exactly as you have stated,
the heat is directly proportional to the
resistance and the square of the current.
So the question is, what happens if we
decrease the resistance? Resistance and
current are related by "Ohm's law",
V = I*R,
that is the voltage potential (V) across a
circuit is equal to the current (I) flowing
through a circuit times the resistance (R) of the
circuit. So if we have a circuit with a constant
potential and we decrease the resistance by a
factor of 1/2, then the current flowing through it
will double. If we try plugging this into the
power equation, we'll see that the power of the
new reduced resistance circuit increases by a
factor of 2 we shown below:
P=(1/2)*R*(2*I)^{2}
P = (1/2)*R*4*I^{2}
P = 2*R*I^{2}
Because the current term is squared in the
power equation, the heat given off by the circuit
is more highly dependent on the current flowing
through it than the resistance. The heat given
off by the new reduced resistance circuit
increases.
I hope this answers your question.
Regards,
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