[[The Bare Essentials of Electrical Engineering.pdf#page=9&offset=99,702|The Bare Essentials of Electrical Engineering, The Basic Trio: Power, Current, and Voltage]] # Voltage - Voltage is the work necessary to move a unit charge from one point to another. Can be written mathematically as $v=\frac{dw}{dq}$ - Can simply represent shorthand notation for voltage difference - Can also refer to the voltage difference between a point & reference point w/ assigned voltage of $0V$ -> reference point called the ground, often applied to lowest point in circuit - Voltage applied across a conductor forces $e^-$ to stop moving randomly and follow the direction imposed by the general field - Closing switch for potential difference applied to conductor resulting in net movement of $e^-$ towards + terminal of voltage source - By definition of current, $vi=\frac{dw}{dq} \frac{dq}{dt}=\frac{dw}{dt}=p$ where $p$ is current # Current - Flow rate of free $e^-$ in conductor is referred to as the electric current, defined as $i(t)=\frac{dq(t)}{dt}$ - Can find total charge flow between $t$ and $t_{0}$ with $q(t)=\int _{t_{0}} ^t i(t)~ d{t}$ - When trying to find unknown current, practically always necessary to *assume* its direction - If you define a direction and get a negative value, the actual direction of current is opposite of what you assumed # Sources - Battery creates $F=q\mathcal{E}$ of any charge $q$ inside it. If $q>0$, $F$ is in the direction of applied $E$ field - When current enters device thru positive voltage node, called passive sign convention, power absorbed treated as negative -> $p_{abs}=vi,p_{del}=-vi$ - Load (passive device): element that absorbs positive power, has positive current entering thru its positive node - Source (active device): positive current enters device from its negative terminal, delivers positive power, active sign convention -> $p_{del}=vi,p_{abs}=-vi$ - Independent sources are unaffected by the circuit they're connected to - Dependent sources have values determined by other quantities in a circuit - Can depend on a $v$ or $i$ at any part in the circuit - Not off the shelf elements but rather simplified models of practical devices # Circuit Structure - Open circuit indicates that current is not flowing - Short circuit used to bypass an element by adding a wire to provide an easier path for current to flow thru - Series: same current flows thru all devices w/ different voltage - Parallel: same voltage flows thru all devices w/ different current - Ideal voltage sources cannot be connected in parallel but can be in series - Ideal current sources cannot be connected in series but can be in parallel