## 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 *### R1

,### R2

, ...,### 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

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