# ECE 140: Linear Circuits ## Voltage, current, and resistance 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. $$i=\frac{dq}{dt}\approx \frac{\Delta q}{\Delta t}$$ ### Power Power represents the rate of doing work, in unit watts ($\pu W$, \pu{J/s}) $$P=\frac{dw}{dt}$$ 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. $$P_{CB}=-P_{BC}$$ In a closed system, conservation of energy applies: $$\sum P_\text{in}=\sum P_\text{out}$$ The **ground** is the "absolute zero" voltage with a maximum potential difference. It is also known as the "reference voltage". ### 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.

(Source: Wikimedia Commons) A **generic current source** provides a known amperage between its two terminals that is defined by the source. The resultant voltage can be calculated.

(Source: Wikimedia Commons) !!! 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 <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. $$ v=kv_0\ |\ ki_0 \\ i=kv_0\ |\ ki_0 $$

(Source: Wikimedia Commons)