Please see [SL Physics 1#Electric potential](/g11/sph3u7#electric-potential) for more information on voltage.
Please see [SL Physics 1#5.2 - Heating effect of electric currents](/g11/sph3u7/#52-heating-effect-of-electric-currents) for more information on current.
Please see [SL Physics 1#Resistance](/g11/sph3u7/#resistance) for more information on resistance.
**Electric charge** $Q$ quantises the charge of electrons and positive ions, and is expressed in coulombs (**C**).
Objects with charge generate electric fields, thus granting potential energy that is released upon proximity to another charge.
!!! warning
Voltage and current are capitalised in **direct current only** ($V$, $I$). In general use, their lowercase forms should be used instead ($v, $i$).
**Voltage** is related to the change in energy ($dw$) over the change in charge ($dq$), or alternatively through Ohm's law:
$$i=\frac{dw}{dq}=\frac{i}{R}$$
**Current** represents the rate of flow of charge in amps (**A**). Conventional current moves opposite electron flow because old scientists couldn't figure it out properly.
- A **ground** is the reference point that all **potential differences are relative to**.
A **generic voltage source** provides a known potential difference between its two terminals that is defined by the source. The resultant current can be calculated.
A **generic current source** provides a known amperage between its two terminals that is defined by the source. The resultant voltage can be calculated.
A current in the **positive direction** indicates that the source is releasing power (is a source). Otherwise, it is consuming power (is a load).
### Dependent energy sources
A **dependent <​T: voltage | current> source** has a **T** dependent on the voltage or current elsewhere in the circuit. $k$ is a function that is likely but not guaranteed to be linear.
A **cathode ray tube** produces an electron beam of variable intensity depending on the input signal. Electrons are deflected by the screen to produce imagery.
- A **supermesh** is a combination of multiple meshes that share a common current source.
Mesh / loop analysis is used to determine unknown currents, using KVL instead of KCL to create a system of equations.
1. Assign mesh currents to each loop.
2. Use KVL and Ohm's law to get voltages in terms of mesh currents.
3. Solve the system of equations.
It may be easier to delete the branch of the current source in supermeshes, treating the region as one mesh with multiple mesh currents.
## Linearity
Circuits are linear if and only if their voltages, resistances, and currents can be expressed in terms of linear transformations of one another. They contain only linear loads, linear dependent sources, and independent souces.
$$\text{output}\propto\text{input}+C$$
!!! example
Halving voltage must halve current (or at least halve it relative to a base current / voltage).
In linear circuits, the superposition principle states that the voltage/current through an element is equal to the sum of the voltages/currents from each independent source alone.
$$
v=\sum v_x \\
i=\sum i_x
$$
To do so, each unused independent source should be replaced with a short circuit (voltage) or an open circuit (current).
In linear circuits, a voltage source in series with a resistor can be replaced by a current source in parallel to that resistor (or vice versa), so long as Ohm's law is followed for the replacement:
$$v_1=i_2R$$
The arrow of the current source must point in the positive direction of the voltage source. This can also be used with dependent sources.
Any part of a circuit including an independent source can be replaced with exactly one voltage source and a resistor in series. Two circuits are **Thevenin equivalent** if their $\lambda$ are equal in $V=\lambda I$.
