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resistors in series

Resistors in Series

In this article we are talking about the resistors in series, how to calculate the equivalent resistance and about the voltage divider. Consider the following picture:

resistors in series

resistors in series and the equivalent resistance (click to enlarge)

In circuit 1 we have 2 resistors R1 and R2 connected in series and in circuit 2 is shown the equivalent resistor Rs. I is the current that flows through the resistors and VB is the voltage of the battery or power supply.

Using the Kirchhoff’s voltage law (KVL) in circuit 1:

VR1 + VR2 = VB   and   I = IR1 = IR2   =>   VB = I * (R1 + R2)

Now we can find the voltage on R1 or R2

VR1 = I * R1 and VR2 = I * R2

Using the Ohm’s Law in circuit 2:

VB = I * Rs   =>   VB = Vs   =>   R1 + R2 = Rs

The equivalent total resistance (Rs) for resistors in series is the sum of the individual resistors. In our case Rs = R1 + R2, but we can extend it for any number of them. Let’s assume that we have n resistors:

Rs = R1 + R2 + R3 + … + Rn

Voltage Divider Rule

Note in circuit 1 that:

VR1 = I * R1 and I = Vs/Rs where Rs = R1+R2

Vx = (Vs * Rx)/Rs (voltage divider rule)

where Vx is the voltage on Rx.

Example of how to calculate resistors in series

As you can see in circuit 1 where the resistor R1 and resistor R2 are connected in series the current I has the same value thru R1 and R2. Only the voltages are different depending on the values of the resistors. For example let’s consider:

  • R1 = 1KΩ and R2 = 12KΩ
  • VB = 9 Volt from a battery

example to calculate resistors in series

I = V/R => I = VB/R1+R2 => I = 9V/1KΩ+12KΩ

we convert KΩ in Ω

I = 9V/1000Ω+12000Ω => I = 9/13000 = 0.00069A = 0.69mA

and now we can calculate the voltage on R1 and R2

VR1 = 1000Ω * 0.0006923A = 0.6923V

VR2 = 12000Ω * 0.0006923A = 8.3076V

Using the voltage divider rule

VR1 = (Vs * R1)/Rs => VR1 = (9 * 1000)/13000 = 0.69V

VR2 = (Vs * R2)/Rs => VR2 = (9 * 12000)/13000 = 8.30V

3 Comments

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  • francis

    Really Exciting ….. Knowledge has no barrier …..education has no limit.Wish to have more on resistors and other semi conductors. Cheers to the great minds that create them ….

  • Kuberkoos

    Excellent! More articles in the same vein i.e. R in parallel, Inductive and Capacitive reactance, and basic calculations on a mix of the above will prove invaluable to the ‘new’ as well as not-so-new electronic hobbyists – as well as learner technicians which do not have other means of learning the ‘ropes’.

  • Mihai

    În prima formulă de sus [I = IR1 + IR2] curentul prin cele două rezistoare în serie nu este o sumă ci o egalitate(are aceiaşi valoare), deci: I = IR1 = IR2. Aşteptăm corecţia de rigoare. Şi nu este nevoie să se folosească legea lui Kirchhoff ci doar legea lui Ohm.

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