How to Calculate Series and Parallel Resistance

Last Updated: April 10, 2024 Fact Checked

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.

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Series Resistance

Parallel Resistance Cheat Sheet

Method 1

Method 1 of 3:

Series Resistance

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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]
X
Research source}
- The formula for calculating a total of n number of resistors wired in series is:
  
  R _eq = R ₁ + R ₂ + .... R _n
  That is, all the series resistor values are simply added. For example, consider finding the equivalent resistance in the image below ^{[2]
  X
  Research source}
- In this example,
  R ₁ = 100 Ω and R ₂ = 300Ω are wired in series. R _eq = 100 Ω + 300 Ω = 400 Ω

Method 2

Method 2 of 3:

Parallel Resistance

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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]
X
Research source}
- The equation for combining n resistors in parallel is:
  
  R _eq = 1/{(1/R ₁ )+(1/R ₂ )+(1/R ₃ )..+(1/R _n )} ^{[4]
  X
  Research source}
- Here is an example, given R ₁ = 20 Ω, R ₂ = 30 Ω, and R ₃ = 30 Ω.
- The total equivalent resistance for all 3 resistors in parallel is:
  
  R _eq = 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

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1
What it is. A combined network is any combination of series and parallel circuits wired together. ^{[5]
X
Research source} Consider finding the equivalent resistance of the network shown below. ^{[6]
X
Research source}
- We see the resistors R ₁ and R ₂ are connected in series. So their equivalent resistance (let us denote it by R _s ) is:
  
  R _s = R ₁ + R ₂ = 100 Ω + 300 Ω = 400 Ω.
- Next, we see the resistors R ₃ and R ₄ are connected in parallel. So their equivalent resistance (let us denote it by R _p1 ) is:
  
  R _p1 = 1/{(1/20)+(1/20)} = 1/(2/20)= 20/2 = 10 Ω
- Then we see the resistors R ₅ and R ₆ are also connected in parallel. So their equivalent resistance (let us denote it by R _p2 ) is:
  
  R _p2 = 1/{(1/40)+(1/10)} = 1/(5/40) = 40/5 = 8 Ω
- So now we have a circuit with the resistors R _s , R _p1 , R _p2 and R ₇ connected in series. These can now simply be added to get the equivalent resistance R ₇ of the network given to us originally.
  
  R _eq = 400 Ω + 20Ω + 8 Ω = 428 Ω.

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How do I calculate the supply current?

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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.

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How do I connect a resistor to get the minimum resistance?

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Net resistance is minimum when all the resistors are connected in parallel.

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How do I find the equivalent resistance between A and B arranged in a triangle?

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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

Understand resistance. Every material that conducts electrical current has resistivity, which is the resistance of a material to electrical current.
Resistance is measured in ohms . The symbol used for ohms is Ω.
Different materials have different resistance properties.
- Copper, for example, has a resistivity of 0.0000017(Ω/cm ³ )
- Ceramics have a resistivity around 10 ¹⁴ (Ω/cm ³ )
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.
How you wire multiple resistors together makes much difference on the overall performance of a resistive network.
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).

Tips

The equivalent resistance (Req) is always smaller than the smallest contributor for a parallel circuit; it is always greater than the greatest contributor for a series circuit.

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Calculate the resistance using the ohms law or the power law:

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Remember, when resistors are in parallel, there are many different means to an end, so the total resistance will be smaller than each pathway. When resistors are in series, the current will have to travel through each resistor, so the individual resistors will add to give the total resistance for the series.

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- V = R * I - P = V * I we can replace V by RI so..... - P = RI * I - P = R I^2 -Example: a lamp of 75watt lighted by a tension of 220 v, how to find its resistance? 1 - P = V * I - I = P/V => 75/220 = 0.34 ohm - P = RI^2 - 75W = R * 0.34^2 - R = 75/0.1156 = 648A - Let's check if it is the same with the other method. 2 - V = R * I. - R = V/I - R = 220/0.34 = 647A almost the same ;).

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How to Calculate Series and Parallel Resistance

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