Lesson 5: Series-Parallel Circuits

Learning Objectives Apply the rules for analyzing series and parallel circuits to a series-parallel circuit. Compute the total resistance in a series-parallel circuit. Analyze series-parallel circuits for current through and voltage across each component. Analyze the power dissipated by each element in a series parallel circuit and calculate the total circuit power.

Series - Parallel Circuits Branch: Part of a circuit that can be simplified into two terminals (2 nodes). A node is the point of connection between two or more branches. Components between these two terminals: Resistors, voltage sources, or other elements

Series - Parallel Circuits Complex circuits May be separated both series and/or parallel elements Other circuits Combinations which are neither series nor parallel

Series - Parallel Circuits To analyze a circuit Identify elements in series and elements in parallel:

Series - Parallel Circuits To analyze a circuit Identify elements in series and elements in parallel:

RULES FOR ANALYSIS (1) Same current occurs through all series elements. Same voltage occurs across all parallel elements. KVL and KCL apply for all circuits, whether they are series, parallel, or series-parallel.

RULES FOR ANALYSIS (2) 4. Redraw complicated circuits showing the source at the left-hand side. 5. Label all nodes. 6. Solve the problem…

It will help… Develop a strategy Best to begin analysis with components most distant from the source Simplify recognizable combinations of components Determine equivalent resistance RT

It will help… Solve for the total current Label polarities of voltage drops on all components Calculate how currents and voltages split between elements in a circuit Verify your answer by taking a different approach (when feasible)

The Series-Parallel Network

The Series-Parallel Network FIRST: Identify elements in series and elements in parallel 20Ω, 30Ω, and 8Ω are in parallel This parallel combination is in series with 2Ω and 6Ω

The Series-Parallel Network SECOND: Simplify and redraw the circuit

The Series-Parallel Network

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

The Series-Parallel Network

The Series-Parallel Network

Example Problem 1 Determine the Rbc of this network:

Example Problem 2 Determine ITOT, I1, I2, Vad

Example Problem 3 Determine ITOT, I1, I2, Vab

Example Problem 4 Determine the unknown voltages in the network below:

Solution Steps Determine equivalent resistance RT Solve for the total current IT Label polarities of voltage drops on all components Calculate how currents and voltages split between elements in a circuit Verify your answer by taking a different approach (when feasible)

Common Mistakes Applying VDR E in the VDR is the voltage across JUST the series elements Rtotal refers to just the combination of the resistors that are series that you know the total voltage across.

Example Problem 5 Determine the voltage drop across the R4 resistor (Vcd) using the VDR. Determine power dissipated by each resistor and verify total power = sum of all power dissipated.

Power Calculations To calculate the power dissipated by each resistor, use either VI, I2R, or V2/R Total power consumed in a Series-Parallel Circuit is the sum of the individual powers Compare with IT2RT

Common Mistakes Applying CDR REQ refers to just the combination of the resistors that are in parallel that you know the total current through. Not using all impedances in the branch

Example Problem 6 Determine I2 using the CDR. Find Va, Vbc

Example Problem 7 Determine ITOT, I1, Va, Vad