Resistors are devices which finds applications in almost every circuit you can imagine. However, sometimes the desired value of resistance is not available commercially. Lets say, you design a circuit which requires 25 kΩ resistor to achieve the desired value of current. But the resistor of 25kΩ is not manufactured commercially. So this shouldn’t be the end of the world for you. You can still achieve the desired value of resistance by connecting resistors in series (and/or parallel).
In this article we shall study in detail the following things about series connection of resistors.
1. How are resistors connected in series? or What exactly is meant by series connection of resistors? These are the first and foremost things we shall discuss in detail.
2. Next, we shall try to find the equivalent resistance of resistors connected in series. Don’t know what is equivalent resistance? Don’t worry, we shall discuss that in detail.
3. Third thing you should understand is how the division of voltage takes place in series connected resistors.
4. Power consideration in series connected resistor. This is the most important point to be kept while implementing above concepts practically.
Series connection of resistors.
When resistors are connected in a chain-like fashion, they are said to be connected in series. Figure given below shows example of resistors connected in series.
In series connection, one end of a resistor is connected with one end of another resistor. Since resistors are bidirectional devices, it doesn’t matter which end of the resistor is connected with the other.
In many practical applications, you will find complex connection of resistors. Some of the resistors might be connected in series and some might be connected in parallel. You should be able to figure out which resistors are connected in series (and/or parallel). Always look for the following condition when you want to make sure the resistors are in series.
If the following condition is true, the resistors are connected in series : If one end of the resistor is connected with one end of another resistor and the same current flows through both the resistors, then they are connected in series. Take a look at the figure below which explains the above point.
In figure (a), one end of resistor R1 is connected with one end of R2. The current flowing through R1 also flows through R2, hence R1 and R2 are in series. In figure (b), one end of resistor R1 is connected with one end of R2 (and R3). However notice that the current through R1 gets divided between branches consisting of R2 and R3. Hence R1 is not in series with R2 (or R3). Here R1 is connceted in series with parallel combination of R2 and R3. So whenever you are confused about series connection of resistors, always look for this condition. If the current gets split between different branches, the resistors are not in series.
Now that you know how to connect resistors in series, let us discuss the concept of equivalent resistance.
Equivalent resistance of resistors connected in series
Resistors connected in series can be replaced by a single resistor without affecting the behavior of circuit. Yes, thats correct. If you connect 2,3,4,…or n number of resistors connected in series, it can all be replaced by a single resistor without affecting the behavior of circuit. The resistance of such a resistor is called “equivalent resistance”. Let us now find out how to calculate the equivalent resistance of resistors connected in series.
Refer the circuit given above. Resistor R1 and R2 are connected in series.The current flowing through them is I. Hence the voltage drop across R1 will be IR1, and the current flowing through R2 will be IR2. The voltage drop across both the resistors must be equal to the voltage supplied by the battery.
Hence V = IR1 + IR2
V = I(R1 + R2)
V/I = R1 + R2
V is the voltage across the battery and I is the current supplied by the battery. Hence the ratio V/I indicates the total resistance “seen” by the battery. If we denote the total resistance with R, then R = R1 + R2. Hence if the value of resistance R1 is 10kΩ and the value of R2 is 20 kΩ, the equivalent resistance of series combination would be 30kΩ.
From the above calculation, we can conclude that the equivalent resistance of resistors connected in series is equal to the sum of all the resistors connected in series. If n resistors are connected in series, then the equivalent resistance is given by
R = R1 + R2 + R3 + ….+Rn.
Keep in mind that when we replace series resistors with its equivalent, then the current through the circuit will not be affected. Refer the figure shown below. In part (a), three resistors are connected in series. The current through the circuit is I. In part (b), we replace the circuit with equivalent resistance. The current flowing through the circuit is still I. The current remains unchanged.
The reverse condition is also true. One resistor can be placed by series connection of resistors, provided the sum of all the resistors must be equal to that of the original resistor.
Division of voltage across series connected resistors.
Uptil now we have studied how to connect resistance in series and we know how to calculate equivalent resistance. Now let us find how the division of voltage takes place in series connected resistors. The voltage across individual resistors can be found out by applying Ohm’s law. In the previous section, we saw how to find equivalent resistance of resistor. It is the sum of all the resistors connected in series. Consider the figure below.
The current flowing through the circuit is
I = V/ (R1 + R2)
Hence the voltage across resistor R1 will be equal to V1 = V * R1/ (R1 + R2) and the voltage across resistor resistor R2 will be V2 = V * R2 / (R1 + R2).
Power consideration in series connected resistors.
Resistors in series can be replaced by their equivalent resistance. However, you must take one factor into consideration i.e., power. If you don’t take this factor into consideration, you might end up damaging the circuit. Let us take an example to understand the above point.
Figure (a) consists of two resistors connected in series. Both the resistors are 100 Ω, 0.25 W. Those resistors can dissipate a maximum of 0.25 W. If we calculate the power dissipated by each resistor in figure (a), it comes out to be 0.202 W. This is below the maximum rating of 0.25 W and hence the circuit is safe to operate. Now consider the situation where you might think that the two series connected 100 Ω resistors can be replaced by a 200 Ω resistor. So you take a 200 Ω, 0.25 W resistor and connect the circuit as shown in figure (b). The value of resistance (200 Ω) is completely correct. But what about power? The power dissipated by the resistor in figure (b) will be 0.405 W. This is above the maximum rating of resistor. So if you connect a 200Ω, 0.25 W resistor, then you might damage the circuit. The resistor of 0.25 W might get too hot and damage the circuit. In such a case, it is advisable to use a resistor with a high wattage rating. A resistor of 0.5 W should be used in such a condition.
This covers all the necessary aspect of series connected resistors. In case of any doubts, do let us know through comments. We would be glad to help you.