109 lines
4.1 KiB
Markdown
109 lines
4.1 KiB
Markdown
# ECE 140: Linear Circuits
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## Voltage, current, and resistance
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Please see [SL Physics 1#Electric potential](/g11/sph3u7#electric-potential) for more information on voltage.
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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.
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Please see [SL Physics 1#Resistance](/g11/sph3u7/#resistance) for more information on resistance.
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**Electric charge** $Q$ quantises the charge of electrons and positive ions, and is expressed in coulombs (**C**).
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Objects with charge generate electric fields, thus granting potential energy that is released upon proximity to another charge.
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!!! warning
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Voltage and current are capitalised in **direct current only** ($V$, $I$). In general use, their lowercase forms should be used instead ($v, $i$).
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**Voltage** is related to the change in energy ($dw$) over the change in charge ($dq$), or alternatively through Ohm's law:
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$$i=\frac{dw}{dq}=\frac{i}{R}$$
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**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.
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$$i=\frac{dq}{dt}\approx \frac{\Delta q}{\Delta t}$$
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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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$$P=\frac{dw}{dt}$$
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It is also directly related to voltage and current:
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$$P=vi$$
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Much like relative velocity, power is directional and relative, with a positive sign indicating the direction of conventional current.
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$$P_{CB}=-P_{BC}$$
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In a closed system, conservation of energy applies:
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$$\sum P_\text{in}=\sum P_\text{out}$$
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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
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!!! definition
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- A **ground** is the reference point that all **potential differences are relative to**.
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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.
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<img src="https://upload.wikimedia.org/wikipedia/commons/f/ff/Voltage_Source.svg" width=100>(Source: Wikimedia Commons)</img>
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A **generic current source** provides a known amperage between its two terminals that is defined by the source. The resultant voltage can be calculated.
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<img src="https://upload.wikimedia.org/wikipedia/commons/b/b2/Current_Source.svg" width=100>(Source: Wikimedia Commons)</img>
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!!! tip
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A current in the **positive direction** indicates that the source is releasing power (is a source). Otherwise, it is consuming power (is a load).
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### Dependent energy sources
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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.
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$$
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v=kv_0\ |\ ki_0 \\
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i=kv_0\ |\ ki_0
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$$
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<img src="https://upload.wikimedia.org/wikipedia/commons/5/55/Voltage_Source_%28Controlled%29.svg" width=100>(Source: Wikimedia Commons)</img>
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<img src="https://upload.wikimedia.org/wikipedia/commons/f/fe/Current_Source_%28Controlled%29.svg" width=100>(Source: Wikimedia Commons)</img>
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### Applications
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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.
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<img src="/resources/images/crt.png" />
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### Resistance
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A **resistor** *always absorbs power*, so must be oriented such that current goes into the positive sign.
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According to Ohm's law, the voltage, current, and resistance are related:
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$$v=iR$$
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The **conductance** of a resistor is the inverse of its resistance, and is expressed in siemens ($\pu{S}$)
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$$G=\frac 1 R = \frac I V$$
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Therefore, power can be expressed by manipulating the equations:
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$$
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\begin{align*}
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P &= IR^2 \\
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&= V^2G \\
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&= \frac{V^2}{R}
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\end{align*}
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$$
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## Kirchoff's laws
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!!! definition
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- A **node** is any point in the circuit to which 3+ elements are *directly* connected (i.e., all junctions).
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- A **supernode** is any connected group in the circuit to which 3+ elements are *directly* connected.
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- A **loop** is any closed path of elements.
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