Difference Between DC Series And Parallel Circuits

A closed path in which electric current flows is called an electrical circuit. An electrical circuit is made up of various elements like energy sources (battery, generator, etc), conductors (used to carry current), and loads. These elements are connected in different ways, where the source supplies electrical energy to the load, which is then converted to other forms of energy.

An electrical circuit in which direct current (d.c.) flows is called a DC circuit. In a DC circuit, current always flows in one direction, i.e., from the positive terminal to the negative terminal of the source.

Based on how circuit elements are interconnected to each other, there are different types of electrical circuits, such as series circuit, parallel circuit, open circuit, short circuit, etc. In this article we learn about comparison between a DC series circuit and a DC parallel circuit.

DC Series Circuit :

A DC series circuit is one in which several components are connected one after the other or end to end across a source of supply, such that there will be only one path for the flow of current, as shown in the figure below. This type of connection is also called a cascade connection.

In the above figure, resistors R₁, R₂, R₃ are connected in series across a voltage source V. Let I current is flowing through all of them, the total voltage applied is equal to the sum of the voltage drops across each resistor.

V = V_{1} + V_{2} + V_{3}

Since the current flowing through all the resistors is same, according to Ohm's law voltage drops across the resistors are given by, V₁ = IR₁, V₂ = IR₂, and V₃ = IR₃ respectively. From the above equation, equivalent resistance R_eq of the circuit is given by,

I R_{eq} = I R_{1} + I R_{2} + I R_{3}

R_{eq} = R_{1} + R_{2} + R_{3}

Therefore, from the above equation, the total or equivalent resistance in a dc series circuit is equal to the sum of the individual resistances. If there are 'n' resistors connected in series, the equivalent resistance R_eq is expressed as,

R_{eq} = R_{1} + R_{2} + R_{3} + \dots + R_{n}

DC Parallel Circuit :

In a DC parallel circuit, components are connected in such a way that one end of each component is connected together to form one junction point, and another end of each component is connected together to form another junction point. These two junction points are then connected across the supply source as shown in the figure below.

In the above figure, three resistors R₁, R₂ and R₃ connected in parallel across voltage source V. If I is the current flowing through the circuit and this current gets divided into I₁ flowing through R₁, I₂ flowing through R₂, and I₃ flowing through R₃ such that I = I₁ + I₂ + I₃. As voltage V is appearing across each of these three resistors, applying Ohm’s law we can write as,

I = I_{1} + I_{2} + I_{3} = \frac{V}{R_{1}} + \frac{V}{R_{2}} + \frac{V}{R_{3}} (i)

If R_eq is the equivalent resistance of the three resistors connected in parallel. Then,

I = \frac{V}{R_{eq}} (ii)

From equations (i) and (ii), we get,

\frac{V}{R_{eq}} = \frac{V}{R_{1}} + \frac{V}{R_{2}} + \frac{V}{R_{3}}

\frac{1}{R_{eq}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}

Therefore, from the above equation of equivalent resistance, if there are 'n' resistors connected in parallel, the equivalent resistance R_eq is expressed as,

\frac{1}{R_{eq}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + \dots + \frac{1}{R_{n}}

Comparison of DC Series and Parallel Circuits :

DC Series Circuit	DC Parallel Circuit
In a series circuit, number of components are connected end to end across a source of supply.	In a parellel circuit, several components are connected across one another.
The same current flows through each component.	The current through each component is different.
The voltage across each component is different.	The same voltage exists across each component.
The sum of the voltages across all the components is equal to the supply voltage. $V = V_{1} + V_{2} + V_{3} + \dots + V_{n}$	The sum of the current flowing through all the component is equal to the supply current. $I = I_{1} + I_{2} + I_{3} + \dots + I_{n}$
The equivalent resistance of dc series circuit is given by, $R_{eq} = R_{1} + R_{2} + R_{3} + \dots + R_{n}$	The equivalent resistance of dc parallel circuit is given by, $\frac{1}{R_{eq}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + \dots + \frac{1}{R_{n}}$
The value of equivalent resistance is larger than the each of the resistances connected in series.	The value of equivalent resistance is smaller than the smallest resistance connected in parallel.
In a series circuit, if one component fails, current stops flowing in the entire circuit.	In a parallel circuit, there are multiple paths for the current to flow. Hence, if one component fails, the circuit can still operate.

Conclusion :

In this article, we have learnt about DC series and parallel circuits. In a series circuit, components are connected end to end so that there is only one path for the current to flow, whereas in a parallel circuit, there will be multiple paths for the electric current to flow.

In a series circuit, current will be same through all the components, and supply voltage will be equal to the sum of the individual voltage drops across all components. In a parallel circuit, voltage across all components remains same, and the total current will be the sum of individual currents flowing through all components.

Difference Between DC Series And Parallel Circuits - Comparison

DC Series Circuit :

DC Parallel Circuit :

Comparison of DC Series and Parallel Circuits :

Conclusion :

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