Colbyn's School Notes
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Basic Electrical Quantities
Charge
Conductors and insulators
Current
$$\begin{equation}
\begin{split}
i &= \frac{\mathrm{d}q}{\mathrm{d}t}
\end{split}
\end{equation}$$
Voltage
Power
Power is defined as the rate energy (U) is transformed or transferred over time. We measure power in units of joules/second, also known as watts.
$$\begin{equation}
\begin{split}
\text{power} &= \frac{\mathrm{d}U}{\mathrm{d}t}
\end{split}
\end{equation}$$
An electric circuit is capable of transferring power.
- Current is the rate of flow of charge
- voltage measures the energy transferred per unit of charge
We can insert these definitions into the equation for power:
$$\begin{equation}
\begin{split}
\text{power}
&= \frac{\mathrm{d}U}{\mathrm{d}t}\\
&= \frac{\mathrm{d}U}{\mathrm{d}q}\cdot\frac{\mathrm{d}q}{\mathrm{d}t}\\
&= v \cdot i
\end{split}
\end{equation}$$
Electrical power is the product of voltage times current. in units of watts.
Standard Electrical Units
SI base units
| Name | Symbol | Quantity |
|---|---|---|
| meter | \(\mathrm{m}\) | length |
| kilogram | \(\mathrm{kg}\) | mass |
| second | \(\mathrm{s}\) | time |
| ampere | \(\mathrm{A}\) | electric current |
| kelvin | \(\mathrm{K}\) | temperature |
| candela | \(\mathrm{cd}\) | luminous intensity |
| mole | \(\mathrm{mol}\) | amount of substance |
SI derived units used in electricity
| Name | Symbol | Quantity | In terms of other SI units |
|---|---|---|---|
| coulomb | C | charge | \(\mathrm{A}\cdot\mathrm{s}\) |
| watt | W | power | \(\frac{\mathrm{J}}{\mathrm{s}}\) |
| volt | V | voltage (electric potential difference) | \(\frac{\mathrm{W}}{\mathrm{A}}\) |
| ohm | Ω | resistance, impedance | \(\frac{\mathrm{V}}{\mathrm{A}}\) |
| farad | F | capacitance | \(\frac{\mathrm{C}}{\mathrm{V}}\) |
| henry | H | inductance | \(\frac{\mathrm{Wb}}{\mathrm{A}}\) |
| hertz | Hz | frequency | \(s^{-1}\) |
| siemens | S | conductance | \(\frac{\mathrm{A}}{\mathrm{V}}\) or \(\frac{\mathrm{1}}{\mathrm{Ω}}\) |
| weber | Wb | magnetic flux | \(\mathrm{V}\cdot\mathrm{s}\) |
| tesla | T | magnetic field strength | \(\frac{\mathrm{Wb}}{\mathrm{m^2}}\) |
Ampere
Coulomb
Electron charge
Watt
Volt
Ohm
Ideal Circuit Elements
Resistor (R)
$$\begin{equation}
\begin{split}
v = i \cdot R
\end{split}
\end{equation}$$
Capacitor (C)
$$\begin{equation}
\begin{split}
i = C \frac{\mathrm{d}v}{\mathrm{d}t}
\end{split}
\end{equation}$$
Inductor (L)
$$\begin{equation}
\begin{split}
v = L \cdot \frac{\mathrm{d}i}{\mathrm{d}t }
\end{split}
\end{equation}$$
Ideal Sources
Ideal Voltage Source
$$\begin{equation}
\begin{split}
TODO
\end{split}
\end{equation}$$
Ideal Current Source
$$\begin{equation}
\begin{split}
TODO
\end{split}
\end{equation}$$