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How to Calculate Resistors in Series and Parallel

Resistors in Series

When resistors are connected one after each other this is called connecting in series. This is shown below.

resistors_in_series_1

To calculate the total overall resistance of a number of resistors connected in this way you add up the individual resistances. This is done using the following formula:

Rtotal = R1 + R2 +R3 and so on.

Example: To calculate the total resistance for these three resistors in series.

resistors_in_series_2 Rtotal = R1 + R2 + R3
= 100 + 82 + 1 Ohms
= 183 Ohms

 

Task 1:

Calculate the total resistance of the following resistor in series.

resistors_in_series_3 Rtotal  = _______________
 = _______________

 

resistors_in_series_4 Rtotal  = _______________
 = _______________

 

resistors_in_series_5 Rtotal  = _______________
 = _______________

Resistors in Parallel

When resistors are connected across each other (side by side) this is called connecting in parallel. This is shown below.

resistors_in_series_6

Two Resistors in Parallel

To calculate the total overall resistance of a of two resistors connected in this way you can use the following formula: resistors_in_series_7

Example: To calculate the total resistance for these two resistors in parallel.

resistors_in_series_8


 

Task 2:

Calculate the total resistance of the following resistor in parallel.

resistors_in_series_9

Three or more resistors in parallel

resistors_in_series_10

To calculate the total overall resistance of a number of three or more resistors connected in this way you can use the following formula:

resistors_in_series_11

Example: To calculate the total resistance for these three resistors in parallel

resistors_in_series_12


 

Task 3:

Calculate the total resistance of the following resistor in parallel.

resistors_in_series_13


 

Answers

Task 1

1 = 1492 Ohms

2 = 2242 Ohms

3 = 4847 Ohms

Task 2

1 = 5 Ohms

2 = 9.57 Ohms

3 = 248.12 Ohms

Task 3

1 = 5.95 Ohms

2 = 23.76 Ohms

 

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28 thoughts on “How to Calculate Resistors in Series and Parallel”

  • Hi! I was just wondering about these parallel resistor equations. Isn't the answer to Task 3 question 1 suppose to be 6 instead of 5.95? Or am I just totally lost here?

    Have a good one!

    Reply
    • HI Elias,

      It comes down to rounding. We rounded to three significant figures, but if you round shorter than that you will see an answer of around 6, so you have done it right.
      Given the value of standard resistors anyway in this case you would probably use 6.8 Ohms.

      Hope that helps.

      Reply
  • What is the formula if I know what resistance I want to achieve but don't have the correct value available. But I do have lots of other value resistors that I might be able to use?

    Reply
    • Hi Colin,

      Simply work the formula backwards.

      For series start with the value you want to achieve, subtracting values you have as you go until you reach 0.

      For parallel what we're dealing with is reciprocal numbers, and they can be reversed. For example 1/33 = 0.30303. 1/0.30303 = 33. So start with the value you want to achieve. Take a resistor value you have and divide 1 by that value to get the reciprocal number.

      Rob

      Reply
      • Hi i read this reply to colin and didnt quite understand.

        What do you do once you have the reciprical values for example my taget is 15 i have 2 resisitors 48 and 80. Recipricals are 1/48=0.208333333 and 1/80=0.0125 what do i do from here?

        Reply
  • Edwin mothibeli May 26, 2016 at 8:20 am

    This is very helpful,thank you for the initiative

    Reply
  • Manuna Kawkni July 16, 2016 at 1:21 am

    very important in my training.

    Reply
  • so for parallel circuits with >2 resistors, there is no algebraic equation derived that we can use. We only do the specific calculation to find the specific answer every time?

    Reply
    • Hi Bill, you would use the series calculation first to find the combined resistances. So, in this case, R1 becomes R1Total and R2 becomes R2Total and you can then do the parallel calculation as normal. I hope this helps.

      Reply
  • for parallel circuit with two resistor we only use that formula in task 2 we do not use it when we have three or more resistors?

    Reply
  • thanks,mark.

    Reply
  • Patrick Lummumba Sunu May 27, 2018 at 10:37 pm

    This is awesome

    Reply
  • Ian De La Cruz June 1, 2018 at 11:21 pm

    I need your help to find the correct formula . I have 3 parallels and one other on its own. I’m sorry I don’t know the correct terminology but all have a value of 60 ohms . I got an A side and B side : on the A side I have the 60 alone and on the B side I have 3 - 60 ohms. I’m pretty good at math but the formula is missing here. Please help me with a formula to figure out the total resistance

    Reply
    • Mark Donnison June 4, 2018 at 2:13 pm

      Hi Ian, it's difficult to visualise your circuit without seeing it but I will give an answer based on what I think you have. Firstly, you will need to work out the value of the three resistors in parallel (the formula is on the page above). Then, once you have this value you then need to do an in series calculation using the resistor on its own and the result of the first calculation you did to give the total resistance for the circuit. I hope this helps.

      Reply
  • sikander lal walia July 13, 2018 at 8:21 am

    How to calculate the value of 3 and more resistors in parallel and elaborate the same.

    Reply
    • Mark Donnison July 17, 2018 at 2:22 pm

      Hi, thanks for getting in touch. The information that you require is included in the above tutorial. Where it says 'and so on', this indicates that the process is the same for additional resistors. I hope this helps.

      Reply
  • Just for fun: task 3 example 1 should be 6 Ohms
    Also formula for two res in paralel and for more than 2 is exactly the same - if you use the latter for two, but solve it with vulgar fractions without finding smallest denominator, you will get the same formula. So, its also possible to make formulas for each on n numbers of resistors, but its impractical for normal use. P.e. for 3 res Rtot=R1xR2xR3/((R1xR2)+(R2xR3)+(R1xR3))

    Reply
  • Really I will your instructions is a very helpful .thanks a lot sir

    Reply
  • nice calculations

    Reply
  • no explanation May 24, 2019 at 4:21 am

    no explanation on the calculation for the 3 parallel resistor, pointlesss, just hocus pocus and assume everyone gets it

    Reply
    • Mark Donnison May 24, 2019 at 11:50 am

      Hi, there is a worked example that shows how to insert your values into the formula and how to take it forwards to an answer. Which bit of the process isn't clear, perhaps we can look at editing the example to highlight this.

      Reply
  • thank you

    Reply
  • Hi! I'm confused because the method my classmate use in solving Parallel Resistors are different from this. I prefer this method because I can understand it well and used this when I'm in Grade 5. So my question is do we get the same answer if I use this method and my classmates will use the method where they will find its denominator?

    Reply
    • Mark Donnison June 27, 2019 at 5:07 pm

      Hi, without seeing how your classmate is arriving at an answer it is impossible to say. However, this is the correct way and if you do it this way you know that you will arrive at the correct answer. I hope this helped.

      Reply
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