1	Chapter 7 Series-Parallel Circuits
2	The Series-Parallel Network Branch Part of a circuit that can be simplified into two terminals Components between these two terminals Resistors, voltage sources, or other elements
3	The Series-Parallel Network Complex circuits May be separated both series and/or parallel elements Other circuits Combinations which are neither series nor parallel
4	The Series-Parallel Network To analyze a circuit Identify elements in series and elements in parallel In this circuit R₂, R₃, and R₄ are in parallel This parallel combination Series with R₁ and R₅
5	The Series-Parallel Network
6	The Series-Parallel Network In this circuit R₃ and R₄ are in parallel Combination is in series with R₂ Entire combination is in parallel with R₁
7	Analysis of Series-Parallel Circuits Rules for analyzing series and parallel circuits still apply Same current occurs through all series elements
8	Analysis of Series-Parallel Circuits Same voltage occurs across all parallel elements KVL and KCL apply for all circuits Whether they are series, parallel, or series-parallel
9	Analysis of Series-Parallel Circuits Redraw complicated circuits showing the source at the left-hand side Label all nodes
10	Analysis of Series-Parallel Circuits Develop a strategy Best to begin analysis with components most distant from the source Simplify recognizable combinations of components
11	Analysis of Series-Parallel Circuits Determine equivalent resistance R_T Solve for the total current Label polarities of voltage drops on all components
12	Analysis of Series-Parallel Circuits Calculate how currents and voltages split between elements in a circuit Verify your answer by taking a different approach (when feasible)
13	Analysis of Series-Parallel Circuits Combining R₂ and R₃ in parallel Circuit reduces to a series circuit Use Voltage Divider Rule to determine V_ab and V_bc. Note that V_bc = V₂ is the voltage across R₂ and R₃ Calculate all currents from Ohm’s Law.
14	Analysis of Series-Parallel Circuits
15	Analysis of Series-Parallel Circuits To find voltage V_ab, Redraw circuit in simple form Original circuit Two parallel branches
16	Analysis of Series-Parallel Circuits V_ab Determined by combination of voltages across R₁ and R₂, or R₃ and R₄ Use Voltage Divider Rule to find two voltages Use KVL to find V_ab
17	Analysis of Series-Parallel Circuits
18	Analysis of Series-Parallel Circuits To find currents in the circuit First redraw the circuit Move source branch all the way to left Reduce circuit to a series circuit
19	Analysis of Series-Parallel Circuits
20	Analysis of Series-Parallel Circuits Voltages Use Ohm’s Law or Voltage Divider Rule Currents Use Ohm’s Law or Current Divider Rule
21	Analysis of Series-Parallel Circuits
22	Bridge Circuit Circuit has R_x = 15 kW Determine V_ab Redraw circuit as shown on slide
23	Bridge Circuit Voltage Divider Rule Determine V_a and V_b. Ground reference point Take at bottom of circuit V_ab = 0.5 V
24	Bridge Circuit R_x is a short circuit (0 W) Voltage Divider Rule Determine V_R₁ V_R₂ = 10 V V_ab = 8 V
25	Bridge Circuit R_x is open Find V_R₁ We know V_R₂ = 0 V No current through it V_ab = –2 V
26	Transistor Circuit Transistor Device that amplifies a signal Operating point of a transistor circuit Determined by a dc voltage source We will determine some dc voltages and currents
27	Transistor Circuit
28	Transistor Circuit Apply KVL: V_BB = R_BI_B + V_BE + R_EI_E Using I_E = 100I_B, we find I_B = 14.3 mA. Other voltages and currents can be determined
29	Potentiometers Example of variable resistor used as potentiometer Volume control on a receiver Moveable terminal is at uppermost position V_bc = 60 V At the lowermost position V_bc = 0 V
30	Potentiometers
31	Potentiometers V_bc changes If load is added to circuit At upper position V_bc = 40 V At the lower position V_bc = 0 V