# SerialLy Connected Resistors

Serially connected resistors cause a common current to pass through them when they are chained together on a single line.

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Stand-alone resistors can be connected in serial connection, parallel connection or both serial and parallel combinations to produce more complex resistance networks, the equivalent resistance of which is a mathematical combination of single interconnected resistors.

Resistance is not only a basic electronic component that can be used to convert a voltage into a current or a current into a voltage, but also by correctly adjusting its value, a different task can be given to the converted current and/or resistances for use in voltage reference circuits and applications that allow it.

Resistances in serial or complex resistance networks can be replaced with a single equivalent resistance R_{EQ} or impedance Z_{EQ,} and regardless of the combination or complexity of the resistance network, all resistors comply with the same basic rules defined by *the Ohm Act* and *Kirchhoff's Circuit Laws.* You can reach our Ohm law calculation application from the link below.

## SerialLy Connected Resistors

Resistors are connected as "Serial" when chained to a single line.Since there is no other way of all the current flowing from the first resistance, it must also pass through the second resistance and the third resistance.Next, there is a **Common Current** that passes through the resistors in the series, since the current flowing from one resistance should flow from others, since it can only follow one path.

The amount of current passing through a series of connected resistors will be the same at all points in a series resistance network.Therefore:

In the example above, their resistance R_{1,} R_{2} and R_{3} allow joint current flow between A and B, which are connected serially between all points.

If there are only serially connected resistors in the circuit, the sum of the single resistors should give the total resistance.

and taking the single values of the resistors in our simple example above, total equivalent resistance, R_{EQ} we can calculate as follows:

R_{EQ} = R _{1} + R _{2} + R _{3} = 1kΩ + 2kΩ + 6kΩ = 9kΩ

Thus, we see that we can replace all three different resistances above with a single "equivalent" resistance, which will have a value of 9kΩ. The fact that the number of resistances is more or less does not change the method of calculating the equivalent resistance in serial circuits, it is calculated in the same way if 2 is in resistance, 22 is in resistance.

This total resistance is generally known as **Equivalent Resistance** and can be defined as follows; " *A single resistance value that can change any number of resistances connected to the series without changing the current or voltage values* in the circuit ".Then, when connecting the resistors in series, the equation given to calculate the total resistance of the circuit is given as follows:

R_{total} = R_{1} + R_{2} + R_{3} + ….. R_{n}

The ohm value and_{R total} value of single resistors act exactly the same way as the circuit.

If the two resistors or impedances in the series are equal and of the same value, the total or equivalent resistance, R _{T} , is equal to twice the value of a resistance.In this example, if the number of resistances in the series was equal to three, the total resistance would be 3R.

In series, the total impedance and total resistance of resistances whose two resistors or impedances are unequal and of different values are obtained directly by collecting

An important point to remember about resistances in serial networks to check the accuracy of mathematics.Total resistance (R, _{T} series connected to two or more resistors) will always be greater than the maximum resistance value in **a larger** chain.In our example above, R _{T} = 9kΩ, the greatest value resistance here is only 6kΩ.

## Serial Resistance Voltage

The voltage on each serially connected resistance complies with different rules than that of the current.We know that the total supply _{} voltage on the resistors from the above circuit is equal to the sum of the potential differences between R _{1} , R _{2} and R 3 , V _{AB} = V _{R1} + V _{R2} + V _{R3} = 9V.

Using the Ohm Act, the voltage between single resistors can be calculated as follows:

Along R_{1}voltage = IR _{1} = 1mA x 1kΩ = 1V

R_{2}alongvoltage = IR _{2} = 1 mA x 2kΩ = 2V

Along R_{3}voltage = IR_{3} = 1 mA x 6kΩ = 6V

the total voltage is equal to the value of 1V + 2V + 6V ) = 9V supply voltage between V_{AB.}Then the sum of the potential differences between the resistors is equal to the total potential difference in the combination, and in our example this is 9V .

The equation given for the calculation of the total voltage in a series circuit, which is the sum of all individual voltages added together, is given as follows:

Then serial resistance networks can also be considered "voltage dividers", and a series resistance circuit with *N-resistant* components will have N-different voltages while maintaining a common current.

Using the Ohm Law, the voltage, current or resistance of any series of connected circuits can be easily found, and the resistance of a series circuit can be changed without affecting the total resistance, current or strength of each resistance.

### SerialLy Connected Resistors Question Sample 1

Using the Ohm Law, calculate equivalent series resistance, serial current, voltage drop and power for each resistance in the following resistors in serial circuit.

All data can be found using the Ohm Act and we can present it in a table to make life a little easier.

resistance | Current | Voltage | Power |

R _{1} = 10Ω | I_{1} = 200mA | V _{1} = 2V | P _{1} = 0.4 W |

R, _{2} = 20Ω | I_{2} = 200mA | V _{2} = 4V | P _{2} = 0.8 W |

R, _{3} = 30Ω | I_{3} = 200mA | V _{3} = 6 V | P _{3} = 1.2 W |

R, _{T} = 60Ω | I_{T} = 200mA | V _{S} = 12V | P _{T} = 2.4W |

Then for the above circuit R _{T} = 60Ω , I _{T} = 200mA , V _{S} = 12V and P _{T} = 2.4W

## Voltage Divider Circuit

From the example above, we can see that different voltages or voltage drops appear in each resistance within the serial network, despite the fact that the supply voltage is given as 12 volts.There is an important advantage to serially connecting resistors in this way through a single DC source, different voltages appear in each resistance and create a very useful circuit called the **Voltage Divider Network.**

This simple circuit divides the feed voltage proportionally along each resistance in the serial chain with the amount of voltage drop determined by the resistance value, and as we now know, the current passing through a series resistance circuit is common to all resistors.Therefore, a larger resistance will have a larger voltage drop on it, while a smaller resistance will have a smaller voltage drop on it.

The series-resistant circuit shown above creates a simple voltage dividing network, producing three voltages : 2V, 4V and 6V from a single 12V feed.Kirchhoff's Voltage Act states that "the supply voltage in a closed circuit is *equal to the sum of all voltage drops (I*R) around the circuit,"* which can be used for good effect.

**The voltage splitting rule**allows us to use resistance proportionality effects to calculate the potential difference between each resistance, regardless of the current that passes through the series.A typical "voltage divider circuit" is shown below.

If more resistance is serially connected to the circuit, different voltages will appear in each resistance according to individual resistance R (Ohm Law **I*R)** values, which provide different but smaller voltage points from a single source.

Therefore, if we had three or more resistances in the serial chain, we can now use our now known potential dividing formula to find the voltage drop between each:

The *voltage dividing circuit* above indicates that the four interconnected resistances are serial.Voltage drop at points A and B can be calculated using the potential divider formula as follows:

We can apply the same idea to a group of resistances in the serial chain.For example, if he wants to find the voltage drop at both ends, we can get R2 and R3 by writing in the paya together.

In this very simple example, resistance can be taken as R1 10%, R2 20%, R3 30%, R4 40% because the voltage drop on a resistance is proportional to the total resistance and in this example the total resistance (R _{T)} is equal to 100Ω or 100%. The application of Kirchhoff's voltage law (KVL) around the closed loop path confirms this.

Now, let's say that we want to use our two resistant potential dividing circuits above to produce a voltage smaller than a larger feed voltage to power an external electronic circuit.Let's say we have a 12V DC source and our impedance circuit with 50Ω only needs a feed of 6V, which is half the voltage.

If we connect the two equal value resistors, each with 50Ω, as a potential dividing network along 12V, this voltage will make the splitting process very nice until we connect the load circuit to the network, but due to the resistance loading effect R, _{L} connected parallel along the _{L} changes its voltage, changing the ratio of two array resistors, and this network cannot be used as a healthy feed, let's examine this situation with the following example:

### SerialLy Connected Resistors Question Sample 3

**Calculate voltage drops between X and Y**

a) When R _{L} is not connected

b) When R _{L} is connected

As you can see above, the output voltage can provide us with the required output voltage of 6V without V _{out} connected load resistance, but when the V _{out} that gives us the same output voltage is connected to a load, it drops to 4V.

Then we can see that a charged voltage divider changes the output voltage as a result of this loading effect for network output voltage.

The effect of lowering a signal or voltage level is known as **Weakening,** so care should be taken when using the voltage dividing network.This loading effect can be compensated and adjusted accordingly using a ponciometer instead of fixed-value resistors.This method also applies to changing tolerances in the resistance structureit also compensates for the voltage divider.

A variable resistance, a pocinciometer or, more commonly called pot, is a good example of a very resistant voltage divider in a single package, as it can be considered thousands of mini resistors in series.Here a constant voltage is applied to the two external fixed connections and variable output voltage is taken from the output terminal.

In addition to being used to calculate a lower supply voltage, the voltage divider formula can also be used for analysis of more complex resistant circuits, which include both serial and parallel branches.The voltage or potential dividing formula can be used to determine voltage drops around a closed DC network or as part of various circuit analysis laws, such as Kirchhoff or Thevenin theorems.

## Serial Connected Resistance Applications

We have seen that serially connected resistors can be used to produce different voltages among themselves, and this type of resistance network is very useful for producing a voltage dividing network.If we replace one of the resistors in the voltage dividing circuit above with a Sensor such as a thermistor, light-dependent resistance (LDR) or even a switch, we can convert a perceived amount of analogue into an appropriate electrical signal.

For example, the following therist circuit has 10KΩ resistance at 25°C and 100Ω resistance at 100°C.Calculate the output voltage ( Vout ) for both temperatures.

### Thermist Circuit

At 25°C

At 100°C

## Summarize

When two or more resistances are connected end-to-end in a single branch, it is said that the resistors are connected to each other in series.Serially connected resistors carry the same current, but the voltage drop between them is not the same as the individual resistance values, as determined by the Ohm Act (V = I*R), which will create different voltage drops in each resistance.

In a series of resistance networks, individual resistors are assembled to give the equivalent resistance (R _{T)} of the serial combination.Resistances in a series of circuits can be changed without affecting the total resistance, current or strength of each resistance or circuit.

In the next tutorial about resistors, we will look at connecting the resistors in parallel and show that the total resistance is the mutual sum of all the resistors added together, and that the voltage is common to a parallel circuit.