3.1 KiB
ECE 140: Linear Circuits
Voltage, current, and resistance
Please see SL Physics 1#Electric potential for more information on voltage.
Please see SL Physics 1#5.2 - Heating effect of electric currents for more information on current.
Please see SL Physics 1#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 (\(\pu W\), )
\[P=\frac{dw}{dt}\]
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)
(Source:
Wikimedia Commons)