How to Add Resistance in Series and Parallel

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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.

Help Calculating Resistance

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:

     R_eq = R₁ + R₂ + .... R_n
     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. R_eq = 100 Ω + 300 Ω = 400 Ω

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1. 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:

     R_eq = 1/{(1/R₁)+(1/R₂)+(1/R₃)..+(1/R_n)}^[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:

     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.

1. 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.

   • We see the resistors R₁ and R₂ are connected in series. So their equivalent resistance (let us denote it by R_s) is:

     R_s = 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 R_p1) is:

     R_p1 = 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 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 R₇ connected in series. These can now simply be added to get the equivalent resistance R₇ of the network given to us originally.

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

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Add New Question

• Question

  How do I calculate the supply current?

  

  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?

  

  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?

  

  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.

• Question

  How do I tell whether or it is in a series or parallel?

  

  If the sum of the resistors is smaller than the smallest resistor, then it is parallel.

• Question

  I have a series of four resistors connected and one in parallel. How do I calculate the total resistance of the circuit given r1=220ohms, r2=130ohms, r4=100ohms, r5=270 in series and r3=470ohms in parallel?

  

  Total Resistance = 1/(All series resistors added together) + 1/(value of parallel resistor). 284 ohms = 1/(1/(220+130+100+270) + 1/(470)).

• Question

  How can I find a current in every branch if four resistors are connected parallel of values (1K,2.2K,3.3K,5.6K) if total current is 10mA?

  

  First calculate your equivalent resistance of this (sub)circuit, which is equal to: 1 / (1/1k + 1/2.2k + 1/3.3k + 1/5.6k) = 516Ohm. So the voltage over a single resistor equals: 10mA * 516Ohm = 5.16V Now, calculate the current through a single resistor, respectively: 5.16V / 1.0kOhm = 5.16mA, 5.16V / 2.2kOhm = 2.35mA, 5.16V / 3.3kOhm = 1.57mA, 5.16V / 5.6kOhm = 0.92mA.

• Question

  A piece of wire of resistance R is cut into n equal parts. These parts are then connected in parallel. If the equivalent resistance of parallel combination is R', then (R/R') is what?

  

  If the wire is cut into n equal parts, the resistance of each part becomes R/n due to decrease in length. When they are connected in parallel, the equivalent resistance becomes R/n^2. So their ratio will be 1/n^2.

• Question

  How do I calculate the total resistance of the resistors?

  

  Resistance1 multiplied by resistance 2, divided by sum of resistance 1 and resistance 2.

• Question

  How do I build a series parallel circuit?

  

  First, take a wire and join it with v volt battery, then join a resistance R1 between wire. Take another resistance of R2 join with the resistance R1 end to end. Take a resistance of R3 and join its one terminal to the wire and one terminal to the end point of the parallel resistance.

• Question

  If 3 resistances of 3 ohms each are connected in parallel, what will be their total resistance?

  

  Adding 1/(1/3+1/3+1/3) will be 1 ohm, since all the resistors are connected in parallel.

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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).

• 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.

• 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.

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

- 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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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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How to Add Resistance in Series and Parallel

Source: https://www.wikihow.com/Calculate-Series-and-Parallel-Resistance

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