Why is Power in an electric circuit equal to $VI$? [closed]

Question

Where did this formula come from? Everyone I asked just told me to substitute values of in ohms law to derive this but no one told why is power equal to voltage * current. Part of the reason for this is because I never understood what is work done in a system and this caused everything from there to not make any sense. Can somebody explain it in layman terms so that my squishy potato brain can understand it?

Answer 1

The level of bad teaching is beyond atrocious.

The question you have is really just down to definitions. $$\begin{align} \tag1\text{Power}&=\frac{\text{Energy}}{\text{time}}\qquad&\qquad P&=\frac Et\\ \tag2\text{Voltage}&=\frac{\text{Energy}}{\text{Charge}}\qquad&\qquad V&=\frac EQ\\ \tag3\text{Current}&=\frac{\text{Charge}}{\text{time}}\qquad&\qquad I&=\frac Qt\\ \tag4&&\therefore\qquad P&=\frac EQ\cdot\frac Qt\\ \tag5&&&=VI \end {align}$$ This holds for the flat DC case.

Later on, we choose the definition of voltages and currents in the AC case so that they make this formula continue to work. Just some clever choice of definitions with the understanding of how the maths would work, to make our lives easier.

That makes this formula basically universal.

Note that I have chosen to give an answer that does not require you to understand what work done is, or what energy is, in the system. Purely just manipulations of definitions. You should still try to make sense of that, but it happens to be unnecessary for this particular bit of understanding.

Answer 2

Very simply,

The voltage (potential difference) between two points measures how much energy is required to move a unit charge from one point to the other.

And current on a path between two points is how much charge is moving between those points per unit time.

So if you multiply these you get how much energy is being used per unit time to move charges between the two points. Which is exactly the definition of power.

Answer 3

Heuristically (without diving into full microscopic theory):

Currents are made by moving charges, the power in classical dynamics is given by the $P= F v$ where $F$ is the force and $v$ is the speed of the particle (in the direction of the force). The force $F$ is the electric field $ E=-\Delta V/\Delta x$ times the electron charge $-e$. The speed is $|\mathbf v|=\Delta x/\Delta t$ and the current is charge per time $e/\Delta t$, so $ev/\Delta x=I$. So $$P=Fv= (-eE) (I \Delta x/e)=I \Delta V.$$