Electronics

Charge

Charge is a fundamental property of matter, which is made out of fermions including electrons. An electron has charge \(e = -1,602*10^{-14}\). Charge in all matter is quantized to be multiples of e.

We denote charge with the letter Q or sometimes q. We measure charge in Coulomb C.

Current

Current in a medium is measured as the amount of charge over a period of time.

\[I =^{def} \lim_{\Delta t \rightarrow 0} \frac{\Delta Q}{\Delta t} = \frac{d Q}{d t}\]

We measure charge with Amperes A where \(1 A = \frac{1 C}{1 s}\).

Voltage

Voltage or sometimes called “potential difference” or just “potential” is defined as:

\[\Delta V = \frac{\Delta U}{Q}\]

It is measured in Volts V where \(1 V = \frac{1 joule}{1 C}\).

This difference depends on where we set the extremes. Usually its value depends on the transformation of energy to heat or light.

You can think about voltage with the classic example of water flow in a pipe.

Generalized Power Law

Since Power is defined as \(P = \frac{d W}{d t}\), we have:

\[P = \frac{d W}{d t} = \frac{d VQ}{d t} = d V I\]

Ohm’s Law

We define Resistance as:

\[R = \frac{V}{I}\]

We measure it in Ohms \(\Omega = \frac{1 V}{1 A}\)

Resistivity and Conductivity

We define Resistivity as:

\[\rho = R \frac{A}{L}\]

Where A is the cross sectional area and L is the length of a wire.

We define conductivity as \(\sigma = \frac{1}{\rho}\).

Then:

\[V = IR = \rho \frac{L}{A} I\]

It is also true that:

\[\begin{split}P = VI = V ( \frac{V}{R} ) = \frac{V^2}{R} \\ P = VI = I (RI) = I^2 R\end{split}\]