See online explanation at AC Circuits

Total Energy Total energy of the system is the sum of the electric and magnetic field energy. CL I B CL ++++  E

RLC Circuit After the switch is closed Kirchoff’s rules gives Solution: Critical Damping: CL I ++++   + R

AC Source The voltage of the power supply follows that of a cosine function. Represent the source as a vector rotating in the complex plane. Real component of vector is the instantaneous voltage. Im Re v VmVm  t VmVm -V m  t v

AC & Resistors Voltage and current are in phase,  = 0. vR v i Im Re v VmVm  t i From Kirchoff

Power Power used by a resistor is Average power is Effective voltage and current are

AC & Inductors Voltage leads current by 90°,  =  /2. Im Re v VmVm  t i v L v i  From Kirchoff Reactance

AC & Capacitors Voltage lags current by 90°,  = -  /2. Im Re v VmVm  t i vC From Kirchoff Reactance v i 

LRC Circuits & AC C L R v Re Im vLvL vCvC vRvR i In a series circuit current is the same everywhere, so add voltages as phasors. Phasors are rotating vectors in the complex plane. Assume we are at t = 0s.

Impedance Re Im vSvS vLvL vCvC vRvR   Express voltage as current times impedance.

ELI the ICE man At resonance,  0, X L =X C and  = 0. For  <  0, the circuit is capacitive and current leads voltage. Also  < 0. For  >  0, the circuit is inductive and voltage leads current. Also  > 0.

Quality Factor As the AC frequency approaches resonance,  0, the current increases. Quality factor indicates how sharp the current peak is around resonance. 00 ImIm Low Q High Q

Transformers A transformer consists of two sets of coils which share the same magnetic flux. AC current through the primary generates a changing magnetic flux, which generates a changing voltage on the secondary. RLRL v PrimarySecondary

Power Lines Ex. How much power is lost if 120V is delivered through a 10  transmission line to a 10  load? Compare that to transmission at 12,000 V and then stepped down to 120V at the load. RLRL 120V 12,000V RTRT RLRL 120V RTRT

Power Transmission Long Distance: 230 kV To Home: 240 V Through Town: 20 kV Less resistive loss at low current.