Network Analysis: Ohm’s Law, Series & Parallel Circuits

Network Analysis is used to determine voltage, current in many electrical circuits. In network analysis, there are a number of components present in the network that are interconnected. Network analysis analyzes the circuit mathematically. Moreover, network analysis is the branch of electrical and electronics engineering. Engineers deal with the circuits in which multiple components as well as power sources are connected. Series and parallel combinations are mostly used in network analysis to find values of parameters. Series and parallel circuits help in analyzing the electrical circuits in physics.

Key Terms: Network analysis, Series and parallel circuits, Ohm’s law, Electric current, Electric circuit, Power sources, Circuit, Voltage

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Network Analysis

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Network analysis is defined as the interconnection of various components in the electrical circuits in physics. Network analysis is used to find the voltage as well as electric current flowing through the various components in the electrical circuits. There are a number of multiple power sources that exist in the network, so to evaluate these kinds of circuits engineers use series and parallel methods. Series and parallel analysis methods are widely used to solve complex circuits. To clearly understand the network analysis let’s see the diagram below:

Electrical Network Diagram 

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Any circuit is considered to be analyzed when all the voltages, as well as currents in different arms, are determined. There are two most common approaches which are used to solve the network:

• Direct Method: Direct method is restricted to solving simple circuits. In a direct method, the circuit is in its original form to determine the different values of voltages and currents. For example, Kirchoff’s law, Nodal analysis, Loop analysis, Superstition theorems etc.
• Network Reduction Method: Network reduction method is used to solve simple as well as complex networks. In the network reduction method, the complex circuit is converted into a much simpler circuit for rapid calculations of different quantities. 

Discover about the Chapter video:

Current Electricity Detailed Video Explanation:

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Network Terminology

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There are many useful terms which are used in electrical networks.Let’s understand these terms with the help of an example.

Electrical Network Example 

• Network: Network is the arrangement of active and passive elements which form closed paths. In the above diagram, ‘abcda’ is the network which forms a closed path.
• Node: In a network, Node is a point where two or more circuit elements are joined together. In the above diagram, ’a’, ‘b’,’c’ and ’d’ are node points or nodes.
• Junction: In a network, a junction is that point where three or more circuit elements are joined. In the above diagram, ‘b’ and ‘d’ are two junction points.
• Branch: In a network, a branch is a point that lies in between the junction points. In other words, a branch is the connection between two nodes. In the above diagram, ‘bcd’, ‘bad’ and ‘bd’ are the branches.
• Loop: In a network, any closed path is known as a loop. In the above diagram, ’abcda’, ’bcdb’ and ‘abda’ are loops in the network.
• Mesh: In a network, a mesh is the complete loop in the circuit which cannot be divided into further loops. In the above diagram, ‘abda’ and ‘bcda’ are the meshes. ‘Abcda’ is not a loop because it includes the other two loops.
• Ports: In a network, ports are commonly the input and output signals. Also, the current in and out from these points. In the above diagram, ‘E1 ‘ and ‘E2’ are the input and output ports.
• Component: In a network, a component is made up of two or more terminals in which current may or may not flow. In the above diagram, ‘R1’, ‘R2’, ‘R3’ are components present in the network.
• Tree: In a network, a tree is a part of the network which is composed of those branches which can be drawn between the junction points without forming any closed path. In the above diagram, the terminal or junction ‘bd’ is forming a tree in the network. 

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Analysis of Various Circuits

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There are many kinds of circuits involved in network analysis. Some of the important circuits which are commonly used in physics are discussed below:

Series Circuit

Series circuits are those circuits in which components (resistor, inductor etc) are connected in series in the network. Also, the electric current flows in each component connected to the circuit. The value of current is the same for all the components present in the network. In this circuit, the value of voltage and current is calculated using ohm’s law. To understand more clearly, let us consider an example:

Series Circuit Diagram

Analysing the Series circuit: In a series circuit, three resistors are connected in a single line with one voltage source. There is only one path for the entrance of the current as well as leaving for the current also. 

Here, 

V_S = voltage source which provides supply to the circuit

R₁ , R₂ , R₃ = three resistors are connected in series

I_S, = electric current flows in the circuit.

According to ohm's law,

V= I x R 

where, 

I = current

R = resistance

Now, V₁ = I_S R₁ (because the value of Is is the same for all the resistance sources)

Similarly, 

V₂ = I_S R₂ and V₃=I_S R₁

Total voltage, V_s = V₁ ,+ V₂ ,+ V₃

Vs  = I_S R₁ + IS R₂ + V₃ = IS R₁

Parallel Circuit 

Parallel circuits are those circuits in which the components (resistor, inductor, capacitor) are connected in parallel in a network. Also, the voltage for each component is the same but the current varies. Current is divided into each component present in the circuit. In this circuit, the value of current is calculated using kirchhoff's current law. To understand more clearly, let us consider an example: 

Parallel Circuit Diagram

Analysing the Parallel Circuit: In the parallel circuit, a single voltage source is used to provide power supply to the network. R₁ and R₂ are present in different arms so that is why current is divided into two arms across the respective resistances.

Here, 

E or V = voltage which provide supply to the circuit

R₁ , R₂ = two resistors are connected in parallel

I₁ = electric current flows across resistor R₁ ,

I₂ = electric current flows across resistor R₂ ,

According to Kirchoff’s current law,

Total current is given by,

 I = I₁ + I₂

We know that, 

I = V/R (as per ohm’s law)

So,

I₁ = V/R₁ and I₂ = V/R₂

Here, ‘E’ is the power source then 

Total current I = I₁ + I₂

I= V/R₁ + V/R₂

I = E/R₁ + E/R₂ 

Bridge Circuit

Bridge circuits are those circuits in which four resistors are connected in such a way that two resistors are in series and two are in parallel with one resistance variable. These resistances are making a bridge shape. Bridge circuits are of basically two types:

• Balanced Bridge Circuit
• Unbalanced Bridge Circuit

To understand bridge circuit let us consider an example:

Analysing the Bridge Circuit: The given diagram illustrates that one source is used to provide power to the network. ABCD is a closed network in which five resistance are connected in such a way that forms a bridge circuit. To solve the bridge circuit we need to split this circuit into two small loops.

Now, if 

R₁/R₄ = R₂/R₅

Then the given circuit is called a balanced bridge circuit and no current flows in the resistance R3 .

If,

R₁/R₄ ≠ R₂/R₅ 

Then the given circuit is called an unbalanced bridge circuit and some current flows in the resistance R₃.

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Things to Remember 

• Network analysis is a tool to measure voltage as well as current in electrical circuits.
• In a series network, the amount of electric current flowing across the components is equal. 
• In a parallel network, the voltage is the same across all the components present in the circuit.
• In a parallel circuit, two resistors which are connected parallel act as current divider.
• When two or more resistors are connected in series then the voltage drop across any resistor is calculated by the voltage divider theorem.
• The voltage is not the same in the series circuit. Total voltage is equal to the sum of voltage across different terminals.
• Any circuit is called a balanced bridge circuit if the ratio of the resistors present in the opposite arms is equal and no current flows in the resistor present at the center.
• Any circuit is called an unbalanced bridge circuit if the ratio of the resistors present in the opposite arms is not equal and some portion of the current flows in the resistor present at the center.

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