1	Chapter 18 AC Series-Parallel Circuits
2	AC Circuits Rules and laws developed for dc circuits apply equally well for ac circuits Analysis of ac circuits requires vector algebra and use of complex numbers Voltages and currents in phasor form Expressed as RMS (or effective) values
3	Ohm’s Law Voltage and current of a resistor will be in phase Impedance of a resistor is: Z_R = RÐ0°
4	Ohm’s Law Voltage across an inductor leads the current by 90°(ELI the ICE man)
5	Ohm’s Law Current through a capacitor leads the voltage by 90° (ELI the ICE man)
6	AC Series Circuits Current everywhere in a series circuit is the same Impedance used to collectively determine how resistance, capacitance, and inductance impede current in a circuit
7	AC Series Circuits Total impedance in a circuit is found by adding all individual impedances vectorially
8	AC Series Circuits Impedance vectors will appear in either the first or the fourth quadrants because the resistance vector is always positive When impedance vector appears in first quadrant, the circuit is inductive
9	AC Series Circuits If impedance vector appears in fourth quadrant Circuit is capacitive
10	Voltage Divider Rule Voltage divider rule works the same as with dc circuits From Ohm’s law:
11	Kirchhoff’s Voltage Law KVL is same as in dc circuits Phasor sum of voltage drops and rises around a closed loop is equal to zero
12	Kirchhoff’s Voltage Law Voltages May be added in phasor form or in rectangular form If using rectangular form Add real parts together Then add imaginary parts together
13	AC Parallel Circuits Conductance, G Reciprocal of the resistance Susceptance, B Reciprocal of the reactance
14	AC Parallel Circuits Admittance, Y Reciprocal of the impedance Units for all of these are siemens (S)
15	AC Parallel Circuits Impedances in parallel add together like resistors in parallel These impedances must be added vectorially
16	AC Parallel Circuits Whenever a capacitor and an inductor having equal reactances are placed in parallel Equivalent circuit of the two components is an open circuit
17	Kirchhoff’s Current Law KCL is same as in dc circuits Summation of current phasors entering and leaving a node Equal to zero
18	Kirchhoff’s Current Law Currents must be added vectorially Currents entering are positive Currents leaving are negative
19	Current Divider Rule In a parallel circuit Voltages across all branches are equal
20	Series-Parallel Circuits Label all impedances with magnitude and the associated angle Analysis is simplified by starting with easily recognized combinations
21	Series-Parallel Circuits Redraw circuit if necessary for further simplification Fundamental rules and laws of circuit analysis must apply in all cases
22	Frequency Effects of RC Circuits Impedance of a capacitor decreases as the frequency increases For dc (f = 0 Hz) Impedance of the capacitor is infinite
23	Frequency Effects of RC Circuits For a series RC circuit Total impedance approaches R as the frequency increases For a parallel RC circuit As frequency increases, impedance goes from R to a smaller value
24	Frequency Effects of RL Circuits Impedance of an inductor increases as frequency increases At dc (f = 0 Hz) Inductor looks like a short At high frequencies, it looks like an open
25	Frequency Effects of RL Circuits In a series RL circuit Impedance increases from R to a larger value In a parallel RL circuit Impedance increases from a small value to R
26	Corner Frequency Corner frequency is a break point on the frequency response graph For a capacitive circuit w_C = 1/RC = 1/t For an inductive circuit w_C = R/L = 1/t
27	RLC Circuits In a circuit with R, L, and C components combined in series-parallel combinations Impedance may rise or fall across a range of frequencies In a series branch Impedance of inductor may equal the capacitor
28	RLC Circuits Impedances would cancel Leaving impedance of resistor as the only impedance Condition is referred to as resonance
29	Applications AC circuits may be simplified as a series circuit having resistance and a reactance AC circuit May be represented as an equivalent parallel circuit with a single resistor and a single reactance
30	Applications Any equivalent circuit will be valid only at the given frequency of operation