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. *R1
,R2
,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.
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