# Formula For Series Parallel Circuit

## # 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 *

,

, 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.

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