Resistors in Series Formula and Voltage Drop Formula

Resistors in Series Formula

We know that resistors are something that resists the current in a circuit. Furthermore, a resistor in a series is a connected resistor in a line. Furthermore, you will learn about resistors, resistors in a series, resistors in a series formula, its derivation and solved examples. Moreover, after completing the topic you will be able to understand resistors in a series.

Resistors

A resistor refers to an electrical component that regulates and limits the flow of electrical current in an electric circuit. Also, we can use it to provide a specific voltage for an active device such as a transistor. Besides, if all the factors are equal then the direct current (DC) circuit, the current through a resistor is directly proportional to the voltage across the circuit and inversely proportional to its resistance.

Resistors in a Series

It is a series of connected resistors which are daisy-chained together in a single line. Subsequently, all the current flowing through the circuit firstly pass through the first resistor and after that, it will pass through the second resistor because it has no other way to go it must and then third and so on.

Also, the resistor series has a common current flowing through them means that the current that flows through the first resistor must also pass through the second resistor and so on because they are in the path of current.

Most noteworthy, the amount of current that flows through a set of a resistor in a series will be the same in the entire series resistor network.

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Resistors in a Series Formula

It is possible to replace a series of a resistor with an equivalent resistor. Also, the equivalent resistance of the number of resistors in a series is the sum of the individual resistance values. Besides, the unit of resistance is Ohm (Ω) that is equal to a volt per Ampere (1 Ω = 1 V/A). Moreover, over larger resistors with kilo-Ohm (1 KΩ=103Ω) or mega-Ohm (1 MΩ=106Ω) resistances are common as well.

Equivalent resistance = resistor 1+ resistor 2 + resistor 3 + …..

Req = R1+R2+R3+⋅⋅⋅⋅

Derivation of the Formula

Req = refers to the equivalent resistance in Ohm or larger unit (Ω )

R1 = refers to the resistance of first resistor in ohm (Ω )
R2 = refers to the resistance of second resistor in ohm (Ω )
R3 = refers to the resistance of third resistor in ohm (Ω )

Solved Example

Example 1

Find the equivalent resistance of a 480.0 KΩ, a 320.0 KΩ, and a 100.0 KΩ resistor connected in series?

Solution:

Req = R1+R2+R3+⋅⋅⋅⋅

∴ Req = R1+R2+R3

Req = 480.0 KΩ + 320.0 KΩ + 100.0 KΩ

Req = 900.0 KΩ

So, the equivalent resistance of the 480.0 KΩ, 320.0 KΩ, 100.0 KΩ resistors in the series is 900.0 KΩ.

Example 2

Two resistors of 240.0 KΩ, and 8.00 MΩ are connected in a series in an electric circuit? Calculate the equivalent resistance?

Solution:

First we need to convert these in common units. Also, in this we need to convert it into mega-Ohms MΩ.

R1 = 240.0 KΩ

R1 = (240.0 KΩ)(103Ω1KΩ)(1MΩ106Ω)

R1 = (240.0) (103106)MΩ

R1 = (240.0) (10+3−6)MΩ

R1 = (240.0) (10−3)MΩ

R1 = 0.2400 MΩ

Now put the values in equivalent resistance formula

Req = R1+R2+R3+⋅⋅⋅⋅

∴ Req = R1+R2

Req = 0.2400mΩ+8.00MΩ

Req = 8.24MΩ

So, the equivalent resistance of 240.0 KΩ, and 8.00 MΩ resistors in a series is 8.24MΩ  

Voltage Drop Formula

The voltage drop identifies the amount of electric power produced or consumed when electric current flows throughout the voltage drop. Also, we can measure it in a circuit with a proper device, but also can be calculated in advance using suitable equations. Moreover, in this topic, we will learn about voltage drop, voltage drop formula, its derivation, and solved examples.

Voltage Drop

It refers to the decrease of electric potential along the path of a current flowing in an electrical circuit. Furthermore, it is a process similar to the electric circuit. Also, each point in the circuit can be assigned a voltage that’s proportional to its ‘electrical elevation’ to speak. In simple words, the voltage drop is the arithmetical difference between a higher voltage and a lower voltage.

In addition, the amount of energy per second (power) delivered to a component in a circuit is equal to the voltage drop from corner to corner of that component’s terminals multiplied by the current flow through the components.

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How to calculate voltage drop?

Voltmeters

One way to resolve the voltage drop across the circuit component is to build the circuit and measure the drop using the voltmeter (current measuring device). Also, they are designed in a way that they disturb the operation of the circuit they are connected to as little as possible. Moreover, they achieve this by minimizing the current that flows through the voltmeter to the smallest possible value.

KCL and KVL

These equations present knowledge of all voltage drops and all current flows in the circuit. Also, the engineers can adjust the various components values to obtain a final circuit that serves its principle in the best possible way.

KCL- Is the Kirchhoff’s Current Law that states that total current flow in and out of any junction of wires in the circuit is zero. Moreover, KCL equations are expressions of charge conservation.

KVL- Is the Kirchhoff’s Voltage Law that states that the sum of voltage drop around any closed path in a circuit is zero. Furthermore, its equations are an expression of energy conservation.

Voltage Drop Formula

The voltage drop formula points out how the supplied power from the voltage source is condensed as electric current flows throughout the elements that do not supply the voltage of the electrical circuit. Moreover, the voltage drops across the internal resistances and connectors of the source are unwanted since the supply energy is lost. Furthermore, the voltage drop across active circuit elements and loads are preferred, because supplied power executes competent work.

V = I × Z
V = IZ

Derivation of the Formula

I = refers to the current in amperes (A)
Z = refers to the impedance in omega (Ω)
V = refers to the voltage drop
Moreover, the single-phase voltage drop formula is given as

VD = 2LRI1000

And three-phase voltage drop formula is given as

VD = 2LRI1000×0.866

Here,

L = refers to the length of the circuit
R = refers to the resistance in Omega (Ω)
I = refers to the load current in amperes

Solved Example on Voltage Drop 

Example 1

Through a circuit, a current of 9A flows through that carries a resistance of 10 Ω. Find the voltage drop across the circuit.

Solution:

Given:

Current = 9A

Impedance Z = 10 Ω

Putting values in the voltage drop formula we get

V = IZ

V = 9 × 10 = 90 V

So, the voltage drop is 90 V.

Example 2

Suppose a lamp has a 15 Ω and 30 Ω connected in a series. Also, a current of 4A is passing through it. So, calculate the voltage drop of the series?

Solution:

I = 4A
Resistance Z = (15 +30) Ω = 45 Ω

Putting values in voltage drop formula we get

V =IZ
V = 4 × 45 = 180 V.

So, the voltage drop is 180 V.