Voltage and Current Source

Mesh Network and Analysis

Superposition Theorem

Thevenin Theorem

Norton Theorem

Maximum Power Transfer Theorem

Reciprocity Theorem

Compensation Theorem

Tellegen Theorem

Voltage Divider

Three Phase System

Star - Delta Transformation

RL Circuit

RL Series Circuit

RL Parallel Circuit

RLC Circuit

Series RLC Circuit

Parallel RLC Circuit

Resonance in Series RLC Circuit

Definition of Electrical Circuit

DC Circuit

Series DC Circuit

Example of Series DC Circuit

Parallel DC Circuit

Example of Parallel DC Circuit

Series and Parallel Circuit

## Electrical DC Circuit

## Definition of Electrical Circuit

An **electrical circuit** is a combination of two or more electrical components which are interconnected by conducting paths. The components may be active or inactive or both. This is a very basic **definition of electrical circuit**.

## DC Circuit

There are two types of electricity - direct current and alternating current, i.e, DC and AC. The circuit that deals with direct current or DC, is referred as **DC circuit** and the circuit that deals with alternating current or AC, is generally referred as AC Circuit. The components of the **electrical DC circuit** are mainly resistive, whereas components of the AC circuit may be reactive as well as resistive. Any **electrical circuit** can be categorized into three different groups - series, parallel and series parallel. So for example, in the case of DC, the circuits can also be divided into three groups, such as **series DC circuit**, **parallel DC circuit** and **series and parallel circuit**.

## Series DC Circuit

When all the resistive components of a **DC circuit** are connected end to end to form a single path for flowing electric current, then the circuit is referred as **series DC circuit**. The manner of connecting components end to end is known as series connection.

Suppose we have n number of resistors R_{1}, R_{2}, R_{3}............R_{n} and they are connected in end to end manner, means they are series connected. If this series combination is connected across a voltage source, the current starts flowing through that single path. As the resistors are connected in end to end manner, the current first enters in to R_{1}, then this same current comes in R_{2}, then R_{3} and at last it reaches R_{n} from which the current enters into the negative terminals of the voltage source. In this way, the same electric current circulates through every resistor connected in series. Hence, it can be concluded that in a **series DC circuit**, the same current flows through all parts of the electrical circuit.

Again according to Ohm's law, the voltage drop across a resistor is the product of its electrical resistance and the current flow through it. Here, current through every resistor is the same, hence the voltage drop across each resistor's proportional to its electrical resistance value. If the resistances of the resistors are not equal then the voltage drop across them would also not be equal. Thus, every resistor has its individual voltage drop in a **series DC circuit**.

The flow of current is shown here by a moving point. This is just a conceptual representation. |

## An Example of Series DC Circuit

Suppose three resistors R_{1}, R_{2} and R_{3} are connected in series across a voltage source of V (quantified as volts) as shown in the figure. Let current I (quantified as Ampere) flow through the series circuit. Now according to Ohm's law,

Voltage drop across resistor R_{1}, V_{1} = IR_{1}

Voltage drop across resistor R_{2}, V_{2} = IR_{2}

Voltage drop across resistor R_{3}, V_{3} = IR_{3}

Voltage drop across whole series DC circuit,

V = Voltage drop across resistor R_{1} + voltage drop across resistor R_{2} + voltage drop across resistor R_{3}

According to Ohm's law, the electrical resistance of an electrical circuit is given by V ⁄ I and that is R. Therefore,

So, effective resistance of the series DC circuit is R = R_{1} + R_{2} + R_{3}. From the above expression it can be concluded, that when a number of resistors are connected in series, the equivalent resistance of the series combination is the arithmetic sum of their individual resistances.

From the above discussion, the following points come out:

- When a number of electrical components are connected in series, the same electric current flows through all the components of the circuit.
- The applied voltage across a series circuit is equal to the sum total of voltage drops across each component.
- The voltage drop across individual components is directly proportional to its resistance value.

## Parallel DC Circuit

When two or more electrical components are connected in a way that one end of each component is connected to a common point and the other end is connected to another common point, then the electrical components are said to be connected in parallel, and such an electrical DC circuit is referred as a **parallel DC circuit**. In this circuit every component will have the same voltage drop across them, and it will be exactly equal to the voltage which occurs between the two common points where the components are connected. Also in a **parallel DC circuit**, the current has several parallel paths through these parallel connected components, so the circuit current will be divided into as many paths as the number of components.

Here in this electrical circuit, the voltage drop across each component is equal. Again as per Ohm's law, voltage drop across any resistive component is equal to the product of its electrical resistance and electric current through it. As the voltage drop across every component connected in parallel is the same, the current through them is inversely proportional to its resistance value.

The flow of current is shown here by a moving point. This is just a conceptual representation. |

## An Example of Parallel DC Circuit

Suppose three resistors R_{1}, R_{2} and R_{3} are connected in parallel across a voltage source of V (volt) as shown in the figure. Let I (Ampere) be the total circuit current which is divided into current I_{1}, I_{2} and I_{3} flowing through R_{1}, R_{2} and R_{3} respectively. Now according to Ohm's law:

Voltage drop across resistor R_{1}, V = I_{1}.R_{1}

Voltage drop across resistor R_{2}, V = I_{2}.R_{2}

Voltage drop across resistor R_{3}, V = I_{3}.R_{3}

Voltage drop across whole parallel DC circuit,

V = Voltage drop across resistor R_{1} = voltage drop across resistor R_{2} = voltage drop across resistor R_{3}

⇒ V = I_{1}.R_{1} = I_{2}.R_{2} = I_{3}.R_{3}

I = I_{1} + I_{2} + I_{3} and as per Ohm's law, I = V ⁄ R hence,

*Thus when a number of resistors are connected in parallel, the reciprocal of the equivalent resistance is given by the arithmetic sum of the reciprocals of their individual resistances.*

From the above discussion of parallel DC circuit, we can come to the following conclusion:

- Voltage drops are the same across all the components connected in parallel.
- Current through individual components connected in parallel, is inversely proportional to their resistances.
- Total circuit current is the arithmetic sum of the currents passing through individual components connected in parallel.
- The reciprocal of equivalent resistance is equal to the sum of the reciprocals of the resistances of individual components connected in parallel.

## Series and Parallel Circuit

So far we have discussed series DC circuit and parallel DC circuit separately, but in practice, the electrical circuit is generally a combination of both series circuits and parallel circuits. Such combined **series and parallel circuits** can be solved by proper application of Ohm's law and the rules for **series and parallel circuit**s to the various parts of the complex circuit.

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