Understanding series resistors

In an electrical circuit, engineers connect the components inside either series or parallel to make a range of useful circuits. With this, we can calculate the voltage, current, and resistance in the circuits. These resistors are said to be connected head-to-tail when in series, and the equivalent overall resistance is the sum of the individual resistance values. In this article, you’ll get to know about the circuit, equation, voltage, applications, and some examples of resistors in series.

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Resistors in series

Resistors are said to be in series when due to their chain arrangement in a single line. This results in a common current passing through them. Here, individual resistors can be connected together in either a series connection. A parallel connection or combinations of both series and parallel can be achieved to produce a more complex resistor network. In the connection, the equivalent resistance is the mathematical combination of the individual resistors connected together.

Note, a resistor is not only a fundamental electronic component used to convert a voltage to a current or a current to a voltage. However, by adjusting its value correctly, a different weighting can be placed onto the converted current and/or the voltage. This is why it can be used in voltage reference circuits and applications. Resistors in series or complicated resistor networks may be replaced by one single equivalent resistor, R_EQ or impedance, Z_EQ. You should know, no matter what the combination or complexity of the resistor network can be, all resistors obey the same basic rules just as stated by Ohm’s law and Kirchhoff’s Circuit Laws.

Furthermore, on the current passing through the circuit, the current flowing through the resistors is common. This is because the current that flows through one resistor must also flow through the others since it flows through only one path. Then, we can say, the amount of current that flows through a set of resistors in series is the same at all points in a series resistor network.

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For example, the resistors R₁, R_2, and R₃ are all connected together in series between points A and B with a common current, I flowing through them.

Diagram of series resistors:

Applications of series resistors

Within a circuit board, the applications of series resistors are so vast since they can be used to produce different voltages across themselves. These types of resistor networks are also useful for producing voltage divider networks. If one of the resistors in the voltage divider circuit is replaced with a sensor such as a thermistor, light-dependent resistor (LDR), or a switch, conversion of an analog quantity being sensed into a suitable electrical signal which has the ability to be measured.

Series resistor circuit

Just as earlier mentioned, as the resistors are connected together in series the same current passes through each resistor in the chain. The total resistance, R_T of the circuit must be equal to the sum of all the various resistors added together. By taking the individual values of the resistors, the total equivalent resistance, R_EQ can be given as:

R_EQ = R₁ + R₂ + R₃ = 1kΩ + 2kΩ + 6kΩ = 9kΩ

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Now you can see how the three individual resistors can be replaced with just one single equivalent resistor that has the value of 9kΩ.

In a case where four, five or 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 and the more resistor added to the series, the greater the equivalent resistance. The equivalent resistance is generally known as total resistance and it 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.

Equation of series equation

The equation is given for calculating the total resistance of the circuit when connecting together resistor in series:

R_total = R₁ + R₂ + R₃ + … R_n etc.

You should know that the total or equivalent resistance, R_T has the same effect on the circuit as the original combination of resistors. This is because it is the algebraic sum of the individual resistances. If two resistances or impedances in series are equal and of the same value, then the total, or equivalent resistance is equal to twice the value of one resistor. In other words, it is equal to 2R and for three equal resistors in series, 3R, etc.

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Also, if two resistors or impedances in series are unequal and of different values, then the total or equivalent resistance, R_T is equal to the mathematical sum of the two resistances. That is equal to R₁ + R₂. If there are three or more unequal (or equal) resistors are connected in series then the equivalent resistance is R1 + R2 + R3 +…, etc.

A voltage of series resistors

In a series-connected resistor, the voltage across each one follows different rules to that of series current. We understand that the total supply voltage across the resistors is equal to the sum of the potential differences across R₁, R_2, and R₃.

V_AB = V_R1 + V_R2 + V_R3 = 9V.

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

Voltage across R₁ = IR₁ = 1mA x 1kΩ = 1V

Voltage across R₂ = IR₂ = 1mA x 2kΩ = 2V

Voltage across R₃ = IR₃ = 1mA x 6kΩ = 6V

Given a total voltage V_AB of (1V + 2V + 6V) = 9V which is equal to the value of the supply voltage. with this, the sum of the potential differences across the resistors is equal to the total potential difference across the combination and 9V. The equation given for calculating the total voltage in a series circuit which is the sum of all the individual voltages added together is given as:

V_Total = V_R1 + V_R2 + V_R3 + …+ V_N

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With this, the series resistor networks can also be thought of as “voltage dividers” and a series resistor circuit have N resistive components will have N-different voltages across it and still maintain a common current. By using Ohm’s Law, the current or resistance of any series-connected circuit can easily be found. Also, the resistor of a series circuit can be interchanged without affecting the total resistance, current, or power to each resistor.

Watch the video below to learn more about resistors in series:

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Conclusion

Resistors are said to be in series when due to their chain arrangement in a single line. This results in a common current passing through them. Individual resistors can be connected together in either a series connection. That is all for this article, where the circuit, equation, voltage, applications, and some examples of resistors are in series.

I hope you get a lot from the reading, if so, kindly share with other students. Thanks for reading, see you around!