# Total Resistance Formula In Series Parallel Circuit

## Total Resistance Formula In Series Parallel Circuit

In a series-parallel circuit, the total resistance is calculated by adding the individual resistances of the series resistors and then subtracting the parallel resistances. The formula for total resistance in a series-parallel circuit is: ``` Rt = R1 + R2 + ... + Rn - (1/R1 + 1/R2 + ... + 1/Rn) ``` where: *

### Rt

is the total resistance of the circuit *

,

, ...,

### Rn

are the resistances of the individual resistors To understand how this formula works, let's look at a simple example. Consider the following series-parallel circuit: In this circuit, there are two resistors in series (R1 and R2) and one resistor in parallel (R3). The total resistance of this circuit can be calculated using the following steps: 1. First, we calculate the resistance of the series resistors: ``` Rs = R1 + R2 ``` 2. Then, we calculate the resistance of the parallel resistor: ``` Rp = 1/(1/R1 + 1/R2) ``` 3. Finally, we add the resistance of the series resistors to the resistance of the parallel resistor to get the total resistance of the circuit: ``` Rt = Rs + Rp ``` In this case, the total resistance of the circuit is: ``` Rt = R1 + R2 + (1/R1 + 1/R2) = 6 + 3 + (1/6 + 1/3) = 10 Ω ``` As you can see, the total resistance of a series-parallel circuit is always less than the sum of the individual resistances. This is because the parallel resistors act to reduce the overall resistance of the circuit. ## Applications of Series-Parallel Circuits Series-parallel circuits are used in a variety of applications, including: *

### Electrical circuits

. Series-parallel circuits are used to connect different components in an electrical circuit, such as resistors, capacitors, and inductors. *

### Electronic circuits

. Series-parallel circuits are used to connect different components in an electronic circuit, such as transistors, diodes, and integrated circuits. *

### Mechanical systems

. Series-parallel circuits are used to connect different components in a mechanical system, such as gears, pulleys, and levers. ## 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: ``` Rt = R1 + R2 + ... + Rn - (1/R1 + 1/R2 + ... + 1/Rn) ``` This formula can be used to determine the total resistance of a series-parallel circuit for any number of resistors.

Simplified Formulas For Parallel Circuit Resistance Calculations Inst Tools

4 Ways To Calculate Series And Parallel Resistance Wikihow

Parallel Resistor Calculator Engineering Calculators Tools

Circuit Topology And Laws Applied Electricity

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

Resistors In Series And Parallel Combination Determination Of The Equivalent Resistance Two Procedure Faqs

Total Resistance Calculator Of Series Parallel Circuit

Parallel Circuits Study Guide Inspirit

Series Circuits And The Application Of Ohm S Law Parallel Electronics Textbook

Series And Parallel Circuits Sparkfun Learn

Electrical Electronic Series Circuits

Series Circuits And The Application Of Ohm S Law Parallel Electronics Textbook

Parallel Circuits And The Application Of Ohm S Law Series Electronics Textbook

Resistance

Dc Parallel Circuits The Engineering Mindset

Series And Parallel Circuits Resistance Total Mnemonic Mammoth Memory

Series And Parallel

Resistors In Parallel Resistor Applications Guide

Series And Parallel Circuits Sparkfun Learn