Introduction

Individual resistors can be connected together in the following manner. Either resistor in series connection, a parallel connection, or combinations of both series and parallel. To produce more complex resistor networks whose equivalent resistance is the mathematical combination of the individual resistors connected together. A resistor is not only a fundamental electronic component. It can be used to convert a voltage to a current or a current to a voltage.

Resistors in series or complicated resistor networks can be replaced by one single equivalent resistor, REQ or impedance, ZEQ. The combination of the resistor network always obeys the same basic rules as defined by Ohm’s Law and Kirchhoff’s Circuit Laws.

Resistors in Series

The Resistors in “Series” when they are daisy-chained together in a single line. Since all the current flowing through the first resistor it must also pass through the consecutive resistors. Then, resistors in series have a Common Current flowing through them. As the current that flows through one resistor must also flow through the others as it can only take one path.

Series Resistor Circuit

As the resistors are connected together in series the same current passes through each resistor in the chain and the total resistance, RT of the circuit must be equal to the sum of all the individual resistors added together. That is R_T=R₁+R₂+R₃

And by taking the individual values of the resistor in our simple example above, the total equivalent resistance, REQ is therefore given as 

R_T=R₁+R₂+R₃=1kΩ + 2kΩ + 6kΩ = 9kΩ

So we see that we can replace all three individual resistors above with just one single “equivalent” resistor which will have a value of 9kΩ.

Where four, five, or even more resistors are all connected together in a series circuit,.The total or equivalent resistance of the circuit, RT would still be the sum of all the individual resistors connected together. The more resistors added to the series, the greater the equivalent resistance (no matter what their value).

This total resistance is generally known as the Equivalent Resistance and can be defined as.  “a single value of resistance that can replace any number of resistors in series without altering the values of the current or the voltage in the circuit“. Then the equation given for calculating total resistance of the circuit when connecting together resistors in series is given as R_T=R₁+R₂+R₃

Series Resistor Equation

Rtotal=R1+R2+R3+…….Rn etc

Note then that the total or equivalent resistance, RT has the same effect on the circuit as the original combination of resistors as it is the algebraic sum of the individual resistances.

two resistances or impedances in series are equal and of the same value, then the total or equivalent resistance, RT is equal to twice the value of one resistor. That is equal to 2R and for three equal resistors in series, 3R, etc.

If two resistances or impedances in series are equal and of the same value, then the total or equivalent resistance, RT is equal to twice the value of one resistor. That is equal to 2R and for three equal resistors in series, 3R, etc.

One important point to remember about resistors in series networks to check that your maths is correct. The total resistance ( RT ) of any two or more resistors connected together in series will always be GREATER than the value of the largest resistor in the chain. In our example above  RT = 9kΩ whereas the largest value resistor is only 6kΩ.

Series Resistor Voltage

The voltage across each resistor connected in series follows different rules to that of the series current. From the above circuit that the total supply voltage across the resistors is equal to the sum of the potential differences across R1, R2, and R3, VAB = VR1 + VR2 + VR3 = 9V.

Using Ohm’s Law, the voltage across the individual resistors can be calculated as:

giving a total voltage VAB of ( 1V + 2V + 6V ) = 9V which is equal to the value of the supply voltage. Then the sum of the potential differences across the resistors is equal to the total potential difference across the combination and in our example this is 9V.

Then series resistor networks can also be thought of as “voltage dividers” and a series resistor circuit having N resistive components will have N-different voltages across it while maintaining a common current.

By using Ohm’s Law, either the voltage, current, or resistance of any series-connected circuit can easily be found and a resistor of a series circuit can be interchanged without affecting the total resistance, current, or power to each resistor.

Example No 1

Use Ohms Law, calculate the equivalent series resistance, the series current, voltage drop and power for each resistor in the following resistors in series circuit.

All the data can be found by using Ohm’s Law, and to make life a little easier we can present this data in tabular form.

Then for the circuit above, RT = 60Ω, IT = 200mA, VS = 12V

After reading this tutorial on “Resistors in Series”. I hope you understood about calculating the series resistance and I am pretty sure you want to know more about electronic circuits and IoT. To know more about IoT you can refer to the following blogs.

• https://www.electronics-tutorials.ws/dccircuits/voltage-divider.html
• https://iot4beginners.com/iot-gateway-a-beginners-guide/
• https://iot4beginners.com/iot-applications-in-transportation/