Summary: Power dissipation in resistor circuits.

We can find voltages and currents in simple circuits containing resistors
and voltage or current sources.
We should examine whether these circuits variables obey the Conservation of
Power principle:
since a circuit is a closed system, it should not dissipate or create
energy.
For the moment, our approach is to investigate first a resistor circuit's
power consumption/creation.
Later, we will *prove* that because of KVL
and KCL *all* circuits conserve power.

As defined on (Reference), the instantaneous
power consumed/created by every circuit element equals the product of its
voltage and current.
The total power consumed/created by a circuit equals the sum of each
element's power.

Consider the simple series circuit should in
(Reference).
In performing our calculations, we defined the current
*any*
resistor equals either of the following.

A physical wire has a resistance and hence dissipates power (it gets warm
just like a resistor in a circuit).
In fact, the resistance of a wire of length
L
L
and cross-sectional area
A
A
is given by
R = ρ L A
R
ρ
L
A
The quantity
ρ
ρ
is known as the resistivity and presents the resistance of a
unit-length, unit cross-sectional area material constituting the wire.
Resistivity has units of ohm-meters.
Most materials have a positive value for
ρ
ρ ,
which means the longer the wire, the greater the resistance and thus the
power dissipated.
The thicker the wire, the smaller the resistance.
Superconductors have zero resistivity and hence do not dissipate power.
If a room-temperature superconductor could be found, electric power could be
sent through power lines without loss!

Calculate the power consumed/created by the resistor

The power consumed by the resistor

We conclude that both resistors in our example circuit consume power, which
points to the voltage source as the producer of power.
The current flowing *into* the source's positive terminal
is

Confirm that the source produces *exactly* the total
power consumed by both resistors.

This result is quite general:
sources produce power and the circuit elements, especially resistors,
consume it.
But where do sources get their power?
Again, circuit theory does not model how sources are constructed, but the
theory decrees that *all* sources must be provided energy to
work.

Comments:"Electrical Engineering Digital Processing Systems in Braille."