3 Finding RT for Series-Parallel Resistances Overview of Series-Parallel CircuitsA series-parallel circuit, or combination circuit, combines both series and parallel connections.Most electronic circuits fall into this category. Series-parallel circuits are typically used when different voltage and current values are required from the same voltage source.Series components form a series string.Parallel components form a parallel bank.
4 Finding RT for Series-Parallel Resistances Overview of Series-Parallel CircuitsThere are three branches in thiscircuit; sections 1 and 2 are series strings.123V
5 Finding RT for Series-Parallel Resistances Overview of Series-Parallel Circuits123VThere are three series sections in thiscircuit; sections 1 and 2 are parallel banks.
7 Finding RT for Series-Parallel Resistances For Fig. 6-1b,The series resistances are:0.5kΩ + 0.5kΩ = 1kΩThe parallel resistances are:1kΩ / 2 = 0.5kΩThe series and parallel values are then added for the value of RT:1kΩ + 0.5kΩ = 1.5 kΩ
9 Resistance Strings in Parallel Series CircuitCurrent is the same in all components.V across each series R isI × R.VT = V1 + V2 + V etc.Parallel CircuitVoltage is the same across all branches.I in each branch R is V/R.IT = I1 + I2 + I etc.
10 Resistance Strings in Parallel I is the samein thissection.VV is the same across each parallel branch.
11 Resistance Strings in Parallel The current in each branch equals the voltage applied across the branch divided by the branch RT.The total line current equals the sum of the branch currents for all parallel strings.The RT for the entire circuit equals the applied voltage divided by the total line current.For any resistance in a series string, the IR voltage drop across that resistance equals the string’s current multiplied by the resistance.The sum of the voltage drops in the series string equals the voltage across the entire string.
13 Resistance Banks in Series To find the total resistance of this type of circuit, combine the parallel resistances in each bank and add the series resistances.VIR=6Ω24V4A6Ω=10 Ω (of R2 + R3)2 branches+ 1Ω (R1)6Ω = 5Ω + 1Ω
14 Resistance Banks and Strings in Series-Parallel To solve series-parallel (combination) circuits, it is important to know which components are in series with one another and which components are in parallel.Series components must be in one current path without any branch points.To find particular values for this type of circuit,Reduce and combine the components using the rules for individual series and parallel circuits.Reduce the circuit to its simplest possible form.Then solve for the needed values using Ohm’s Law.
23 Analyzing Series-Parallel Circuits with Random Unknowns V1 = VA (parallel branches have the same voltage)V1 = 90VorV1 = I1R1 V2 = I2-3R2 V3 = I2-3R3V1 = 3A × 30Ω V2 = 2A(20 Ω) V3 = 2A(25 Ω)V1 = 90V V2 = 40V V3 = 50VNote: V2 + V3 = VA40V + 50V = 90V
24 Analyzing Series-Parallel Circuits with Random Unknowns =RTITVA5A90A18Ω
25 Troubleshooting: Opens and Shorts in Series-Parallel Circuits In series-parallel circuits, an open or short in one part of the circuit changes the values in the entire circuit.When troubleshooting series-parallel circuits, combine the techniques used when troubleshooting individual series and parallel circuits.