Electrical Power and Energy Overview

Electric power
In the case of voltage and current related reference direction, electric power p can be written as p(t)=u(t)i(t)
p >0 indicates that the component absorbs electric energy, and p <0 indicates that the component releases electric energy.
In the case of voltage and current unrelated reference direction, p(t)=u(t)i(t)
p >0 indicates that the component releases electric energy, and p <0 indicates that the component absorbs electric energy

Electrical energy
Units In the International System of Units, current (A), charge (C) — coulomb, voltage (V), electrical energy (J) — joule, power (W) — watt.

Circuit Elements
Lumped element assumptions:

At any time, the current flowing into one terminal of a two-terminal component must be equal to the current flowing out of the other terminal, and the voltage between the two terminals is a single-valued quantity.
The number of terminals can be divided into two-terminal, three-terminal, four-terminal components, etc.

Resistor
A resistor is a component that irreversibly converts electrical energy into other forms of energy (such as heat, mechanical energy, light energy, etc.).
1. Symbol
2. Ohm's Law
(1) The reference direction of voltage and current is set to the same direction

u=Ri R is called resistance, the unit of resistance:  (Ohm)

Let G = 1/RG be called conductivity
. The unit of conductivity is S (Siemens). Then Ohm's law is expressed as i = Gu.

Linear resistance R is a constant that has nothing to do with voltage and current. Volt-ampere characteristic curve:

The volt-ampere characteristic of a resistor element is a straight line passing through the origin.

(2) The reference directions of the voltage and current of the resistor are opposite

Then Ohm's law is written as: u=–Ri or i=–Gu
Note: The formula must be used in conjunction with the reference direction!

Power and Energy
Power:

p absorb = ui = i2 R = u2 / R
p absorb = – ui – ( – Ri ) i = i2 R = – u ( – u / R ) = u2 / R At any time, the resistor element can never emit electrical energy, it can only consume electrical energy. Therefore, the resistor is also called a "passive element" and an "energy-consuming element".

Energy: can be expressed as work. The energy consumed by the resistor from t to t0 is: