How to Calculate Series and Parallel Resistance

Need to know how to calculate series resistance, parallel resistance, and a combined series and parallel network? If you don't want to fry your circuit board, you do! This article will show you how in just a few easy steps. Before reading this, please understand that resistors do not actually have an "inside" and an "outside" to them. The use of "in" and "out" is merely a figure of speech to help novices understand the wiring concepts.

Method 1
Method 1 of 3:

Series Resistance

  1. Image titled Calculate Series and Parallel Resistance Step 1
    1
    What it is. Series resistance is simply connecting the "out" side of one resistor to the "in" side of another in a circuit. Each additional resistor placed in a circuit adds to the total resistance of that circuit.[1]
    • The formula for calculating a total of n number of resistors wired in series is:

      Req = R1 + R2 + .... Rn
      That is, all the series resistor values are simply added. For example, consider finding the equivalent resistance in the image below[2]

    • In this example,
      R1 = 100 Ω and R2 = 300Ω are wired in series. Req = 100 Ω + 300 Ω = 400 Ω

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Method 2
Method 2 of 3:

Parallel Resistance

  1. Image titled Calculate Series and Parallel Resistance Step 2
    1
    What it is. Parallel resistance is when the "in" side of 2 or more resistors are connected, and the "out" side of those resistors are connected.[3]
    • The equation for combining n resistors in parallel is:

      Req = 1/{(1/R1)+(1/R2)+(1/R3)..+(1/Rn)}[4]
    • Here is an example, given R1 = 20 Ω, R2 = 30 Ω, and R3 = 30 Ω.

    • The total equivalent resistance for all 3 resistors in parallel is:

      Req = 1/{(1/20)+(1/30)+(1/30)}

      = 1/{(3/60)+(2/60)+(2/60)}

      = 1/(7/60)=60/7 Ω = approximately 8.57 Ω.

Method 3
Method 3 of 3:

Combined Series and Parallel Circuits

  1. Image titled Calculate Series and Parallel Resistance Step 3
    1
    What it is. A combined network is any combination of series and parallel circuits wired together.[5] Consider finding the equivalent resistance of the network shown below.[6]
    • We see the resistors R1 and R2 are connected in series. So their equivalent resistance (let us denote it by Rs) is:

      Rs = R1 + R2 = 100 Ω + 300 Ω = 400 Ω.

    • Next, we see the resistors R3 and R4 are connected in parallel. So their equivalent resistance (let us denote it by Rp1) is:

      Rp1 = 1/{(1/20)+(1/20)} = 1/(2/20)= 20/2 = 10 Ω

    • Then we see the resistors R5 and R6 are also connected in parallel. So their equivalent resistance (let us denote it by Rp2) is:

      Rp2 = 1/{(1/40)+(1/10)} = 1/(5/40) = 40/5 = 8 Ω

    • So now we have a circuit with the resistors Rs, Rp1, Rp2 and R7 connected in series. These can now simply be added to get the equivalent resistance R7 of the network given to us originally.

      Req = 400 Ω + 20Ω + 8 Ω = 428 Ω.

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Community Q&A

  • Question
    How do I calculate the supply current?
    Community Answer
    Community Answer
    You divide your total voltage by total resistance. For example let's say your voltage is 200V and your total resistance is 25 ohm, so it's IT=VT/ RT=200/25 = 8A.
  • Question
    How do I connect a resistor to get the minimum resistance?
    Community Answer
    Community Answer
    Net resistance is minimum when all the resistors are connected in parallel.
  • Question
    How do I find the equivalent resistance between A and B arranged in a triangle?
    Community Answer
    Community Answer
    Suppose A and B are the extremities of the base of the triangle. The resistor (R 1) between A and B would be parallel with the equivalent resistance of the other two, which are essentially in series. Then, R 2 and R 3 have an equivalent resistance: RE = R 2 + R 3. RE and R 1 are parallel, therefore the equivalent resistance is the reciprocal of the sum of the reciprocals of RE and R 1.
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Some Facts

  1. Understand resistance. Every material that conducts electrical current has resistivity, which is the resistance of a material to electrical current.
  2. Resistance is measured in ohms. The symbol used for ohms is Ω.
  3. Different materials have different resistance properties.
    • Copper, for example, has a resistivity of 0.0000017(Ω/cm3)
    • Ceramics have a resistivity around 1014(Ω/cm3)
  4. The higher the number, the greater the resistance to electrical current. You can see that copper, which is commonly used in electrical wiring, has a very low resistivity. Ceramic, on the other hand, is so resistive that it makes an excellent insulator.
  5. How you wire multiple resistors together makes much difference on the overall performance of a resistive network.
  6. V=IR. This is Ohm's law, defined by George Ohm in the early 1800s. If you know any two of these variables, you can easily calculate the third.
    • V=IR: Voltage (V) is the product of current (I) * resistance (R).
    • I=V/R: Current is the quotient of voltage (V) ÷ resistance (R).
    • R=V/I: Resistance is the quotient of voltage (V) ÷ current(I).

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References

  1. ↑ https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)/10%3A_Direct-Current_Circuits/10.03%3A_Resistors_in_Series_and_Parallel
  2. ↑ https://www.physicsclassroom.com/class/circuits/Lesson-4/Combination-Circuits
  3. ↑ http://physics.bu.edu/py106/notes/Circuits.html
  4. ↑ https://www.omnicalculator.com/physics/parallel-resistor
  5. ↑ https://www.electronics-tutorials.ws/resistor/res_5.html
  6. ↑ https://flexbooks.ck12.org/cbook/ck-12-physics-flexbook-2.0/section/17.5/primary/lesson/combined-series-parallel-circuits-phys/
  7. Handbook for Sound Engineers: The New Audio Cyclopedia, Glen Ballou, Editor

About This Article

MS
Co-authored by:
Mantas Silvanavicius
Licensed Electrician
This article was co-authored by Mantas Silvanavicius. Mantas Silvanavicius is a Licensed Electrician and the Owner of M+S Electric based in Las Vegas, Nevada. With more than 20 years of experience, he specializes in home electrical installations, testing, and wiring. Mantas and his team have completed projects for companies such as Seiko and Springhill Suites by Marriott. M+S Electric is licensed, bonded, and insured. This article has been viewed 1,468,673 times.
73 votes - 68%
Co-authors: 40
Updated: December 14, 2022
Views: 1,468,673
Categories: Electromagnetism
Article SummaryX

To calculate series resistance, which you should use when connecting the "out" side of one resistor to the "in" side of another in a circuit, use the formula Req = R1 + R2 + .... Rn. In this formula, n equals the number of resistors in a series. In order to find the parallel resistance, for when the "in" side and "out" sides of 2 or more resistors are connected, use the formula Req = 1/{(1/R1)+(1/R2)+(1/R3)..+(1/Rn)}. The solution will give you the total resistance for 2 or more resistors. To learn how to calculate resistance in a combined series, keep reading!

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