How To Calculate Resistance In Parallel Circuit?


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This answer presumes that the value of all of the resistors in the circuit is known. The combined resistance in a parallel circuit is less than the value of any of the individual resistors. Depending on the number of resistors in a circuit, and their individual resistances, there are a few different methods to use to calculate the total resistance:
[1] If there are only two resistors in parallel, the formula is pretty straight forward: Rt(total)=R1xR2/R1+R2. Let's say the values of the resistors are R1=10Ω and R2=20Ω. The total resistance would be figured: (10x20)/(10+20) which is 200/30=6.67. The total resistance of this parallel pair of resistors is 6.67Ω.
[2] For a circuit having multiple (any number of) resistors with an equal amount of resistance each, there is another relatively easy formula: R/Rn=Rt (with "R" being the value of ONE of the equal resistors and "n" being the number of resistors). For multiple (equal in value) 20Ω resistors in parallel we get this: 20/Rn=Rt , which is:20/4=Rt , which is: Total R=5Ω.
[3] A circuit with multiple resistors of differing values is more difficult, but easy if broken down and taken one step at a time. The formula for this is: 1/Rt=(1/R1)+(1/R2)+(1/R3). Let's use resistors of 2Ω, 4Ω, and 8Ω: 1/Rt=1(1/2Ω)+(1/4Ω)+(1/8Ω). To add these values, we need to convert these to a common denominator: 1/Rt=(4/8Ω)+(2/8Ω)+(1/8Ω). This gives: 1/Rt=(7/8Ω). Because the Rt in this is a denominator under 1, we need to make the reciprocal (flip it), which must also happen to the other side of the equal sign. This gives: Rt=8/7Ω. Doing the final math (8 divided by seven) gives the total resistance: Rt=1.14Ω.
One reminder - Total resistance in a parallel circuit will always be lower than the lowest valued resistor. A quick way to double check your work.

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