AC

• AC means that the voltage is a sine wave. The electrons in the circuit go one way and then the other and oscillate between these two directions. This is because the voltage from the source constantly switches from being positive to negative

  
• V(t) = Vmax sin(ωt)

  V(t) means that V changes with t, and the right-hand side tells you how. Vmax is the maximum value that the voltage can get up to (positive or negative).

  ω is the angular frequency of the sine wave. (ω = 2πf)
• I(t) = V(t)/ R = Vmax /R sin(ωt) = Imax sin(ωt
• calculate the AC RMS values of voltage and current:

  VRMS = Vmax √2

  IRMS = Imax√2
• PAC = IRMS VRMS
• The reactance of a capacitor

  has the symbol XC and is measured in Ω
• A low frequency means that the charges move onto the plates more slowly. The capacitor has more time to grab and hold onto them. At low f the capacitor is more sticky, so it has a higher reactance. So XC ∝ 1/ω
•  capacitor doesn’t do much to slow the AC current down. The

  AC current can almost pass through the capacitor.

  Even though capacitors pass AC electricity, they still have an AC resistance (they still

  put up a fight). We call this fight

  reactance
• reactance also depends on the capacitance of the capacitor. A lower

  capacitance means that less charge can be stored on the plates for a given voltage. Less charge stored means a greater reactance.

  So XC ∝ 1/C
• reactance in capacitor: XC = 1/ωC
• Capacitor voltage depends on the current. More current means more stored charge on the capacitor, so a bigger voltage exists across the capacitor. It also depends on the reactance of the capacitor – bigger reactance requires a bigger voltage to overcome:

  V = IXc
• The phase difference between current and voltage in ac capacitor circuit is 90° (or π/2)
• The supply voltage leads the capacitor voltage by 90°, but both

  are sine waves

  
• Adding resistor (AC RC): The resistor voltage is VR = IR. So the current still leads

  VC by 90°.

  
•  inductors in an AC circuit have reactance For inductors, we call

  this XL
• angular frequency: a higher angular frequency (remember ω = 2πf) means more change in current. So the inductor will have a higher reactance (because inductors oppose change).

  Inductance: a higher inductance means that the inductor is more sensitive to changing current. So, it will have a higher reactance.

  Together these define inductive reactance: XL = ωL
• Voltage across an inductor in a pure AC inductor circuit:

  V = IXL
• adding a resistor means that the inductor voltage leads the resistor voltage (and therefore current) by 90°. 

  
• RLC circuit: VL leads VR by 90° but VC lags VR by 90°. This means that

  VL and VC subtract because they are 180° apart.

  
• to connect the source voltage VS, the current I, and the R, XC, and

  XL from the resistor, capacitor, and inductor:

  V = IZ
• Z, measured in Ω, is called the impedance of the AC circuit. It’s the total amount that the circuit opposes the flow of charge, made up of the resistor's resistance, the capacitor's reactance, and the inductor's reactance. You can think of it as overall AC resistance

  
• impedance of the RLC circuit has the formula:

  Z =√(XL−XC)²+R²
• XL = XC -> ωL = 1/ωC ω = 1/√LC

  When this happens, the impedance becomes minimum, and the maximum current can get to its biggest value (Imax = Vmax/Z). This is called resonance
• resonant frequency, We call this f0 and the equation is: f0 = 1/2π√LC