# Alternating Current

We invented AC power because they’re much easier and economical to implement than DC power.

12-15-2022: I had this conversation with Chester about electrocution, because my heater keeps

### AC Applied To Resistors

For the resistor of an AC Circuit, there is no lag between the current and voltage (they are in-phase).

$i(t)=I_{m}cos(ωt+θ_{i})$ $v(t)=I_{m}Rcos(ωt+θ_{i})$ We can write this in Phasor domain as $I=I_{m}e_{jθ_{i}}$ $V=I_{m}Re_{jθ_{i}}$ The relationship is given by $V=RI$

We say that the Phasor $V$ and $I$ are in phase since $θ_{v}=θ_{i}$ →The current and voltage oscillate in sync.

### AC Applied to Inductor

For the inductor of an AC Circuit, voltage leads and current follows. $i(t)=I_{m}cos(ωt+θ_{i})$ $v(t)=ωLI_{m}cos(ωt+θ_{i}+2π )$

We can write this in the Phasor domain as $V=jωLI$

$V$ leads $I$ by $2π =90°$ (voltage leads current)

### AC Applied to Capacitor

In capacitor, current leads and voltage follows.

$v(t)=V_{m}cos(ωt+θ_{i})$ $i(t)=ωCV_{m}cos(ωt+θ_{i}+2π )$

We can write this in the Phasor domain as $V=jωCI $

$I$ leads $V$ by $2π =90°$ (current leads voltage)

### AC Frequency, Personal aha moment on Polarity!

In North America, its 60 Hz so it flips back and forth 60 times a second. aha moment! this is why we can plug both ways in the wall socket (Polarity does not matter), cuz its using AC, but DC u gotta be super careful with polarity. See Electrical Outlet