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22 March 2009
Author: Giorgos Lazaridis
Connecting Resistors

Connecting resistors in series

A series circuit is a circuit that all components are connected in series with one's end connected to the other's beginning. The following circuit shows three resistors connected in series:

Total resistance in series connection

The total resistance is the mathematical sum of all resistors and it is bigger than the part with the biggest resistance.

In our previous example, the total RTOTAL is:

RTOTAL = R1 + R2 + R3 = 10 + 15 + 25 = 50 Ohms, in general

RTOTAL = R1 + R2 + ...+ Rn

Current flow in series connection

Current is the same for all parts in the circuit and it is equal to I total.

Using the Ohm's law, you can calculate the total current:


This amount of current is equal for every part. This means that ITOTAL flows through R1, R2 and R3 and it is 10Volts / 50 Ohms = 0.2 Amperes = 200 mA

Voltage drop in series connection

The sum of the voltage drops on every part in a series circuit is equal to the applied voltage.

Every part connected to a power supply causes a voltage drop that can be measured on it's pins. This voltage drop can be calculated by the ohm's law and it is: U = R x I. In a series circuit, every resistor may have different voltage drop measured on it's pins but adding all drops of every component must have the supply voltage. So:

U1 = ITOTAL x R1 = 0.2 x 10 = 2 Volts
U2 = ITOTAL x R2 = 0.2 x 15 = 3 Volts
U3 = ITOTAL x R3 = 0.2 x 25 = 5 Volts

U1 + U2 + U3 = 2 + 3 + 5 = 10 Volts.

In general:

V = U1 + U2 + ... + Un

Connecting resistors in parallel

A parallel circuit is a circuit that all components are connected in parallel, the beginnings and the ends of all components connected together. The following circuit shows three resistors connected in parallel:

Total resistance in parallel connection

The total resistance of the circuit is calculated with the following type and it is smaller than the part with the smaller resistance:

1/RTOTAL = (1/R1) + (1/R2) + ...+ (1/Rn)

In our example:

1/RTOTAL = (1/R1) + (1/R2) + (1/R3) => 1/RTOTAL = 0.2 + 0.1 + 0.05 => 1/RTOTAL = 0.35 => RTOTAL = 2.857 Ohms

An exception that makes our life easier is if we have to calculate only two resistors in parallel. In this case, there is a special type that can calculate the R total and it is:

RTOTAL = (R1 x R2) / (R1 + R2)

It looks more easier to calculate. If we have more than two resistors this type cannot be applied directly. It is possible to calculate the Rtotal in steps by calculating each time two resistors. In our example:

Ra = (R1 x R2) / (R1 + R2) => Ra = 50 / 15 = 3.3333 and RTOTAL = (Ra x R3) / (Ra + R3) => RTOTAL = 66.6666 / 23.3333 = 2.857 Ohms.

Some people do prefer this method as it is easier to calculate it 'by heart' without calculator.

Current flow in parallel connection

The total current drawn by the source is the mathematical addition of each current that flows through every part.

ITOTAL = I1 + I2 + ... +In

where Ixxx is the current that flows in every part of the circuit. In our example, this means that:

I1 = V / R1 = 10 / 5 = 2 Amp
I2 = V / R2 = 10 / 10 = 1 Amp
I3 = V / R3 = 10 / 20 = 0.5 Amp

Voltage drop in parallel connection

Voltage drop is the same for every part in the circuit. Obviously, this is true as every part is connected directly to the power supply. This is very helpful to know when you have some parts like 12Volt lamps to connect to a 12Volt power supply. Connecting them in parallel will make sure that every lamp will have 12Volts on it's pins.

Relative pages
  • Learn how to connect capacitors together
  • The Ohm law
  • Learn how to read the part coded values
  • Learn how the capacitor works
  • The resistor theory
  • The voltage divider theory
  • Dr.Calculus: Carbon film resistors color code calculator
  • Dr.Calculus: Metal film resistors color code calculator
  • Dr.Calculus: Standard resistor values calculator
  • Dr.Calculus: Total resistance calculator
  • Dr.Calculus: Voltage divider calculator

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  • At 15 May 2014, 5:04:38 user MaKr0 wrote:   [reply @ MaKr0]
    • Very confusing: keep changing the values of the resistors in each example... and that may be OK... but then you calculation are based on even more different value no-where referenced to.
      first image shows 10, 20, and 30, but then you calculation are based on 10, 15 and 25
      then the second image shows 5, 10 and 30 but the calculation does not use the last value (30), but something else (20) never shown before as a third value to arrive to 0.05; and again the second calculation (of the parallel resistors) again uses that value (20) to arrive at 66.6666 / 23.3333 instead of the shown value (30) in the image.

      So either the picture example shown are wrong and in need of correction or the calculation use the wrong values and are in need of correction.
      Anyway not very good to explain or teach anything since cannot be followed by a novice since nothing matches with what it is referred to.

      Fix the mistakes and then we are good to go.

  • At 11 November 2010, 10:39:34 user RICK wrote:   [reply @ RICK]

    reddit this Reddit this

     HOT in heaven!

    NEW in heaven!

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