Resistors in Series – Complete Guide

jojo September 27, 2017 6 Comments

Resistor, the most basic yet essential passive component of an electronic circuit, is nothing but a device that restricts the flow of current. So why is it called passive? It is called so because it dissipates power rather than generating it in a circuit. Some practical resistors are shown in the image below. In this article, we are going to learn in detail about Resistors in Series or in simple words a Series Circuit.

Resistors in Series

The figure 1 (above image) shows how they look in reality, but obviously, there will be some schematic way of representing a resistor in a circuit. Usually, in a circuit diagram, you see a component denoted by zigzag lines, which look like that shown in figure 2 (below image); that component is a resistor.  If you are interested to know in-depth about resistors, our article titled” Resistors and type of resistors” will help you.

Resistor Standard Symbol

Figure 2: Resistor Standard Symbol

 

Since resistors obey Ohms law and Kirchhoff’s circuit laws, they are used to convert voltage into current and vice versa. This means by manipulating the value of resistor we can change either of them(voltage or current). But, how can the resistance in a circuit be manipulated? Do we have to choose a different resistor of another value each time we intend to change the voltage/current? This sounds like a tedious task, so is there any simpler method to change the resistance in a circuit? Yes, there is!

Actually, the resistors can just be connected together to form complex resistor networks, that have an effective change in the total resistance of the circuit. They can be wired either in series or in parallel or a combination of both and be replaced by a single equivalent resistor. Therefore, instead of choosing a different resistor every time you want to change it in the circuit, you can just add the available resistors to connect them in series, parallel or combination of both.  This article will help you understand the resistors in series.

How to connect resistors in series?

In order to understand the connection of the resistors in series, let us take two resistors namely R1 and R2.

Let R1 have terminals a1 and b1, and R2 have terminals a2 and b2 (See figure 3)

Resistor Series

Figure 3 – Two Resistors to make series connection

 

Now, if we connect the terminal b1 of resistor R1 and terminal a2 of terminal R2, we would get a daisy chained type resistor network. (See Figure 4)

Series Resistors

Figure 4: Resistors making Series connection

This is how resistors in series look like when they are connected. Also, we can add more resistors in the same fashion. These daisy-chained resistors can be represented as a single resistor, having an effective resistance, Reff. This replacement of series resistors by a single resistor doesn’t change the overall current/voltage.

Resistors in Series

Figure 5: Resistors in Series

 

Resistance in Series

Figure 6:- Effective Resistance in Series

 

 

Ohm’s law in a series resistor circuit:

Let us take three resistors, R1, R2,­ R,connected in series, having an equivalent resistance of Reff, having a voltage of V applied across them, as shown in figure 7. Let I be total the current that flows through the circuit.

Resistors in Series Circuit

Figure 7: Resistors in Series Circuit

 

Then according to ohms law:

From the equation 1, it is quite clear how changing the effective resistance would change the current, I of the circuit.

Next, we need to know how to calculate the effective resistance, for this, first let us see what changes it brings to Voltage and Current, in the circuit.

Voltage and current in a series resistor circuit:

To understand how connecting resistors in series affect the current and voltage, let us assume the following:

V1 , I1 = Voltage and current through resistor R1.

V2, I2 = Voltage and current through resistor R2.

V3,I3 = Voltage and current through resistor R­3.

V, I = Total voltage and current in the circuit. (Refer Figure 8)

Series Resistors

Figure 8 – Resistors in Series Circuit

 

From Kirchoff’s current law, we know that in a circuit, the current flowing into a node and leaving the node must be equal.  However, if we look into our circuit (figure 8), there are no nodes. That means there is only one path for the current to flow in a circuit. Therefore, the current leaving resistor R­, enters resistor R2 and the same current would enter resistor R3.

Thus we can say that:

         I1=I2=I3= I                –> equation(2)

From equation 2, it is clear that the current through all the resistors connected in series is same.

Next, we also know that the individual resistors have individual resistances that are constant and are different.

Therefore according to Ohms law, we can write the voltages across each resistor as:

voltages in series circuit

From equation 3,  it is pretty clear that the voltage across each resistor is different. However, if we use three equal resistors, the voltage across them would be same.

Now, what about the total voltage? This can be answered by just knowing about the Kirchoff’s voltage law.

The law states that according to principle of conservation of energy, the total voltage in a closed circuit is zero.

So here in the closed circuit of fig 8, the KVL can be applied as:

KVL - Kirchoffs voltage law in series resistor circuit

Thus the total voltage applied is the sum of individual voltages across the series resistors.

Now that we know about the current and voltage, let us determine the effective resistance of a series resistors.

Effective Resistance in Series Circuit:

The effective resistance or equivalent resistance of a series of resistors is nothing but a value which can replace N number of resistors connected in series, without changing the overall current and voltage of the circuit.

The circuit shown in figure 8, has 3 resistors in series, namely R1, R2 and R3 .

Now from equations 3 and 4, we have:

V1+V2+V3– V=0

V= V1+V2+V3

IReff = IR1+IR2+IR3

Reff= R1+R2+R3                    –> equation (5)

Equation 5 gives us the value of the effective resistance of 3 resistors connected in series as the sum of the individual resistance of each resistor.  We, see that as we add resistors in series the effective resistance increases.

For N number of resistors in series, the effective resistance is :

Effective Resistance in Series Resistor Circuit

Let us solve some examples that would aid your understanding of the concept.

Example 1:

Suppose you have 4 resistors having same resistance, R, then what would be the effective resistance if they are connected in series?

From equation 6, we can calculate the effective resistance as:

N=4, then This brings us to another equation :

For N number of resistors having same resistance, R , the effective resistance would be

Formula - Resistors in Series

Example 2:

You have 3 resistors of values 5kΩ, 15kΩ and 20kΩ and a voltage supply of 10Volts. Calculate  the current through the circuit for the following cases:

a) When only the 5kΩ resistor is connected to the supply voltage.

b) When all the three resistors are connected in series to the supply voltage.

What can be inferred from the results you have got for cases a) and b)?

a) Here Total resistance will be R1 = 5kΩ and V= 10 Volts

Current through the circuit, I= 10/5k = 2mA.

b) Here the effective / total resistance of the circuit, Reff is = R1 +R2 +R3 = (5k+15k+20k)Ω =40kΩ

Thus the current through the circuit will be

I = V/ Reff = (10/40k) = 0.25mA

From both the results, we see that when a series of resistors were connected to the battery the current through the circuit dipped from 2mA (for case (a))to 0.25mA.

This means that when we add resistors in series the current through the circuit decreases.

Example 3:

For the circuit given below (figure 9), calculate :

(a)effective resistance  (b)current through the circuit (c) voltage across each resistor

Resistance in Series Circuit

Figure 9: Resistances in Series Circuit

(a) Given:

Individual resistances, R1= 8kΩ, R2=2kΩ, R3=10kΩ

Using equation 6,

Effective resistance, Reff = R1+R2+R3 = (8k+2k+10k)Ω = 20k Ω

(b) Current through circuit, I

Given that total voltage applied, V = 20Volt and we have calculated effective resistance as Reff =20kΩ

From equation 1, using ohms law, we have –  V= I*Reff

calculating effective resistance

(c) Voltage across resistors, 

Now that we have current through the circuit, we can find the voltage across each resistor.

Let V1, V2,V3 be the voltage across resistor R1, R2, R3 respectively.

Then ,

V1 = IR1 = (0.5m)×(8k) = 4V

V2 = IR2 = (0.5m) ×(2k) = 1V

V3 = IR3= (0.5m)×10k = 5V

We see that,  V1+V2+V3 = (4+1+5)V = 10V = V. It’s like we have split the supply voltage, as individual voltages across the resistors.

This very fundamental concept is used in the voltage divider circuit.  Let us see how a voltage divider works.

The voltage divider circuit:

For applications where a smaller supply voltage is needed but we have only a higher supply voltage available with us, we can make use of a voltage divider circuit. Here, a series resistance circuit is used to divide the source voltage, among the resistor.  The circuit diagram shown in figure 10, represents a typical voltage divider circuit.

Figure 10 – Voltage Divider Circuit

In order to understand how the voltage is divided in the circuit, let us make use of some mathematical equations:

Referring to the circuit, shown in figure 10, the current flowing through the circuit, I is given by

The voltages across the resistors, R1 and R2 , V1 and V2  respectively can be written as:

This equation is known as the voltage division rule. Here we have taken only two resistors; however, if we take N number of resistors, then we can generalize the equation as:

Voltage Divider Rule

Voltage across Kth resistor, of resistance Rk will be:

Voltage Divider Rule

Let us solve an example that would help you understand voltage division better.

Comments
  • MR OHM 1970
    October 25, 2017

    Some Very Important Theory Is Being Taught Here,,,MANY THANKS!!!!

  • sai Kiran
    September 13, 2017

    knowledgeable topic…….

  • Raghunath
    September 13, 2017

    nice lecture, its useful.

  • gopiteja
    September 13, 2017

    Way of lecture is easy to understand.

  • Lijo George
    September 13, 2017

    Quite knowledgeable..

  • Babalola Emmanuel
    September 7, 2017

    Nice lecture ,atleast have gained something

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