## # Formula for Series Parallel Circuit

A series-parallel circuit is a circuit that contains both series and parallel connections. The total resistance of a series-parallel circuit can be calculated using the following formula: ``` R = R1 + R2 + (R3//R4) ``` where: *### R

is the total resistance of the circuit *### R1

,### R2

, and### R3

are the resistances of the series resistors *### R4

is the resistance of the parallel resistor To use this formula, first find the equivalent resistance of the parallel resistors by dividing the product of their resistances by their sum: ``` R4//R3 = (R4 * R3) / (R4 + R3) ``` Then, add this equivalent resistance to the resistances of the series resistors to find the total resistance of the circuit. For example, consider the following series-parallel circuit: ``` [Image of a series-parallel circuit] ``` The total resistance of this circuit can be calculated as follows: ``` R = 10 Ω + 20 Ω + (40 Ω//20 Ω) ``` ``` R = 10 Ω + 20 Ω + (20 Ω * 40 Ω) / (20 Ω + 40 Ω) ``` ``` R = 10 Ω + 20 Ω + 32 Ω / 60 Ω ``` ``` R = 10 Ω + 20 Ω + 5.33 Ω ``` ``` R = 35.33 Ω ``` Therefore, the total resistance of this series-parallel circuit is 35.33 ohms. ## Applications of Series-Parallel Circuits Series-parallel circuits are used in a variety of applications, including: *### Electrical power distribution

. Series-parallel circuits are used to distribute electrical power to homes and businesses. The series resistors in these circuits help to reduce the voltage drop across the parallel resistors, which ensures that all of the loads in the circuit receive the same amount of power. *### Electronic circuits

. Series-parallel circuits are used in a variety of electronic circuits, such as amplifiers, filters, and oscillators. The series resistors in these circuits help to stabilize the circuit and prevent oscillation, while the parallel resistors provide a path for current to flow when the circuit is turned off. *### Mechanical systems

. Series-parallel circuits are also used in mechanical systems, such as hydraulic systems and pneumatic systems. The series resistors in these circuits help to reduce the pressure drop across the parallel resistors, which ensures that all of the loads in the system receive the same amount of power. ## Conclusion Series-parallel circuits are a common type of circuit that is used in a variety of applications. The total resistance of a series-parallel circuit can be calculated using the formula R = R1 + R2 + (R3//R4). This formula can be used to design and troubleshoot series-parallel circuits.Resistors In Parallel Examples Solutions S Notes

Parallel Circuit Stickman Physics

4 Ways To Calculate Series And Parallel Resistance Wikihow

Series And Parallel Ap Physics 1

Capacitors In Series Parallel And Mixed Explained Nerdytechy

What Is A Series Parallel Circuit Combination Circuits Electronics Textbook

Electrical Electronic Series Circuits

Series Parallel Circuit Examples Easy Analysis Wira Electrical

In A Circuit With Series And Parallel Connection Of Resistors How Should I Calculate For Voltage Drop Quora

Series Parallel Circuit Examples Electrical Academia

Series Parallel Circuit Examples Easy Analysis Wira Electrical

How Do You Calculate The Total Resistance Of A Parallel Circuit Plus Topper

Simple Parallel Circuits

Series And Parallel Circuits Sparkfun Learn

Physics Tutorial Parallel Circuits

Series Parallel Circuit Examples Electrical Academia

Series And Parallel Connection Of Batteries Advantages Disadvantages

Combination Series Parallel Circuits Troubleshooting Motors And Controls

Physics Tutorial Combination Circuits