Series Parallel Circuits

Series Parallel Circuits

• A series parallel circuit combines series and parallel circuits.
• The series portion consists of resistors in a row such as R1 and R4.
• Total current (IT) flows through each series component.
• The voltage drops are proportional to the individual resistance value.
• The parallel portion, such as R2 and R3, divides IT proportionally with the individual branch resistances.
• The equivalent resistance (RE) is smaller than the smallest individual branch resistance.
• RE can only be found when each branch contains one resistive value.
• Branch voltage drops will be equal.
• Series parallel circuits can be redrawn and simplified to a simple series circuit for easier calculations.

Calculating Values in Series Parallel Circuits

• Start by calculating RE using the reciprocal method.
• For the example given, the calculation would look like 6k X⁻¹ + 3k X⁻¹ = X⁻¹ = which gives you 2kΩ for RE.
• The product over sum method can only be used when there are only two branches.
• To find total resistance (RT), add the series resistors to the RE value.
• Ohm's law (V=IR) can be used to find total current (IT = Applied Voltage / RT).
• In the example, 60V / 15kΩ = 4mA.
• To find the voltage drops across series resistors (R1 and R4), multiply the resistor value by IT.
• For R1: 5kΩ * 4mA = 20V.
• For R4: 8kΩ * 4mA = 32V.
• To find the voltage drop across the parallel portion, calculate RE * IT (2kΩ * 4mA = 8V), which is the voltage seen on both branches of the parallel part of the circuit.
• To solve for current in a parallel branch, utilize Ohm's law (I=V/R).

Calculating Values with Multiple Resistors in Each Branch

• First, combine the resistors in each branch.
• For example, if Branch 1 has R2 and R3, add them to get the total resistance of Branch 1.
• Use the reciprocal formula to find the RE of the parallel branches and then add the branch values
• After finding RE, find the RT of the circuit by adding the series resistor R1 to the RE.
• Use Ohm's law to find IT.
• Calculate the voltage drop of R1 (IT * R1).
• Calculate the voltage drop across the parallel branches (RE * IT).
• Use Ohm's law to calculate each individual branch current (branch voltage / branch resistance = branch current).
• Multiply the branch current by the individual resistances in each branch to get their respective voltage drops.

Troubleshooting Series Parallel Circuits: Opens

• An open in the series portion of the circuit causes RT to increase to infinity.
• Current will drop to 0.
• The voltage measurement across the open component will measure the applied voltage.
• If the open is in the parallel portion of the circuit, RE will increase.
• Because RE increases, RT will also increase.
• IT will decrease.
• Series voltage drops will decrease, and parallel voltages will increase.

Troubleshooting Series Parallel Circuits: Shorts

• A short in the series portion of the circuit causes RE to stay the same.
• RT will decrease, and IT will increase.
• The series voltage drop will decrease, and the parallel voltage drops will increase.
• A short in the parallel portion of the circuit eliminates the parallel portion which brings RE to 0.
• RT will decrease because RE decreases.
• IT will increase.
• Series voltage drops will increase, and the parallel branch voltage will drop to 0 volts.