eifueo/docs/1b/ece140.md

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# ECE 140: Linear Circuits
## Voltage, current, and resistance
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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.
$$i=\frac{dq}{dt}\approx \frac{\Delta q}{\Delta t}$$
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### Power
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Power represents the rate of doing work, in unit watts ($\pu W$, \pu{J/s})
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$$P=\frac{dw}{dt}$$
It is also directly related to voltage and current:
$$P=vi$$
Much like relative velocity, power is directional and relative, with a positive sign indicating the direction of conventional current.
$$P_{CB}=-P_{BC}$$
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In a closed system, conservation of energy applies:
$$\sum P_\text{in}=\sum P_\text{out}$$
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The **ground** is the "absolute zero" voltage with a maximum potential difference. It is also known as the "reference voltage".
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### Independent energy sources
!!! definition
- 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.
<img src="https://upload.wikimedia.org/wikipedia/commons/f/ff/Voltage_Source.svg" width=100>(Source: Wikimedia Commons)</img>
A **generic current source** provides a known amperage between its two terminals that is defined by the source. The resultant voltage can be calculated.
<img src="https://upload.wikimedia.org/wikipedia/commons/b/b2/Current_Source.svg" width=100>(Source: Wikimedia Commons)</img>
!!! tip
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 <&ZeroWidthSpace;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.
$$
v=kv_0\ |\ ki_0 \\
i=kv_0\ |\ ki_0
$$
<img src="https://upload.wikimedia.org/wikipedia/commons/5/55/Voltage_Source_%28Controlled%29.svg" width=100>(Source: Wikimedia Commons)</img>
<img src="https://upload.wikimedia.org/wikipedia/commons/f/fe/Current_Source_%28Controlled%29.svg" width=100>(Source: Wikimedia Commons)</img>