# Formula For Parallel Circuit Resistance

## Formula for Parallel Circuit Resistance

The formula for parallel circuit resistance is: ``` Rt = 1 / (1/R1 + 1/R2 + 1/R3 + ...) ``` where: *

### Rt

is the total resistance of the parallel circuit. *

,

,

### R3

, etc. are the resistances of the individual resistors in the parallel circuit. To find the total resistance of a parallel circuit, you can add the reciprocals of the individual resistances and then take the reciprocal of the sum. For example, if you have two resistors in parallel with resistances of 10 ohms and 20 ohms, the total resistance of the circuit would be: ``` Rt = 1 / (1/10 + 1/20) = 1 / (0.1 + 0.05) = 1 / 0.15 = 6.67 ohms ``` The formula for parallel circuit resistance can be used to calculate the total resistance of any number of resistors in parallel. ## Example Problems ### Problem 1 A parallel circuit has three resistors with resistances of 10 ohms, 20 ohms, and 30 ohms. What is the total resistance of the circuit? ``` Rt = 1 / (1/10 + 1/20 + 1/30) = 1 / (0.1 + 0.05 + 0.033) = 1 / 0.183 = 5.46 ohms ``` ### Problem 2 A parallel circuit has four resistors with resistances of 10 ohms, 20 ohms, 30 ohms, and 40 ohms. What is the total resistance of the circuit? ``` Rt = 1 / (1/10 + 1/20 + 1/30 + 1/40) = 1 / (0.1 + 0.05 + 0.033 + 0.025) = 1 / 0.218 = 4.59 ohms ``` ### Problem 3 A parallel circuit has five resistors with resistances of 10 ohms, 20 ohms, 30 ohms, 40 ohms, and 50 ohms. What is the total resistance of the circuit? ``` Rt = 1 / (1/10 + 1/20 + 1/30 + 1/40 + 1/50) = 1 / (0.1 + 0.05 + 0.033 + 0.025 + 0.02) = 1 / 0.238 = 4.21 ohms ``` ## Conclusion The formula for parallel circuit resistance is a simple and straightforward way to calculate the total resistance of a circuit with multiple resistors in parallel. By adding the reciprocals of the individual resistances and then taking the reciprocal of the sum, you can quickly and easily find the total resistance of any parallel circuit. Parallel Circuits And The Application Of Ohm S Law Series Electronics Textbook Parallel Circuits Advantages Power Cur Voltage And Effective Resistance Parallel Resistor Capacitor Circuits Reactance And Impedance Capacitive Electronics Textbook Special Case Of Two Resistors In Parallel Physics Homework Help Assignments And Projects Tutors Online Dc Parallel Circuits The Engineering Mindset Resistors In Series And Parallel Formula Derivation Owlcation Series And Parallel Circuits How To Solve Parallel Circuits 10 Steps With Pictures Wikihow Parallel Circuits And The Application Of Ohm S Law Series Electronics Textbook Can You Derive An Equivalent Resistance For A Series And Parallel Combination Of Resistors Quora 5 3 Simple Parallel Circuits How Do You Calculate The Total Resistance Of A Parallel Circuit Plus Topper Wiring Diagrams Mojo Shout Why Are Resistances Added In Inverse Parallel Circuits Unlike A Series Circuit Electricity Quora 5 Ways To Calculate Total Resistance In Circuits Wikihow How To Solve Parallel Circuits 10 Steps With Pictures Wikihow Parallel Circuit Cur Calculations Inst Tools 4 Ways To Calculate Series And Parallel Resistance Wikihow How To Calculate The Voltage Drop Across A Resistor In Parallel Circuit Sciencing