Circuits

• closed path that allows for flow of electrons
• movement of electrons -> current (amps) and drift

Current §

Current is defined as

$$I=\frac{\Delta q}{\Delta t}=\frac{neA\Delta d}{\Delta t}$$

where $n$ is the number of electrons per meter cubed, $e$ is the charge, and $A$ is the cross sectional area.

The speed of electrons is called drift velocity and is defined as follows

$$V_d=\frac{\Delta d}{\Delta t}$$

Current runs opposite to the flow of electrons.

Current Density §

Current density is the amount of current passing through a cross section of the conductor.

$$J=\frac{I}{A}$$

Power §

Power is defined as energy over time. Since we know that voltage is energy per charge, and current is charge over time, power is

$$\begin{array}{rl}P=\frac{dU}{dt}& =\frac{dU}{dq}\cdot \frac{dq}{dt}\\ & =VI\\ & =I^{2}R\\ & =\frac{V^2}{R}\end{array}$$