# The Basic Laws and Theorems in Electrical Circuit Network Analysis

### Key Takeaways

• Electrical circuit network analysis is the process by which the circuit's electrical parameters are calculated.

• Nodal analysis is the method used in circuit analysis to determine the voltages at nodes in a circuit.

• Mesh analysis is governed by Kirchhoff’s voltage law and is suitable for planar circuits or networks.

Many practical circuits are made up of memoryless elements such as resistors, capacitors, and inductors

Many practical circuits are made up of memoryless elements such as resistors, capacitors, and inductors. The elements in these electric circuits are connected to each other and consume power from the voltage or current sources. These interconnected elements form electric circuits and can be solved using the concepts of series and parallel circuits to obtain quantities of interest such as voltage, current, power, etc. Unfortunately, such techniques are time-consuming in large networks. To make electrical circuit network analysis easier, several techniques can be used.

## Electrical Circuit Network Analysis

Electric circuits can be DC circuits, AC circuits, or a combination of both. In practical applications, we use both AC and DC circuits involving inductors, capacitors, and resistors. Depending on the application, the number of passive components (resistors, inductors, and capacitors) in the circuit varies.

Electrical circuit network analysis can be defined as the process by which the circuit's electrical parameters, such as voltage, current, equivalent resistance, total power losses, etc., are calculated. Using the known elements or parameters, the unknown parameters or quantities in the circuit are determined through analysis.

All circuits can be analyzed as either series circuits or parallel circuits. However, in doing so, the time taken to solve the circuit increases with the increase in complexity of the circuit. It is essential to use techniques that make circuit analysis easier.

Let’s look at the basic laws used in electric circuit problem-solving before we discuss the various methods of circuit analysis.

## Ohm’s Law

George Ohm formulated the relation between electromotive force to the current flowing in the circuit, called Ohm's Law. By applying Ohm’s Law to circuits, the electrical resistance offered by the circuit to the flow of current can be determined.

Electrical resistance is an important physical property associated with circuits. Based on the calculation of the electrical resistance of the circuit, the parts of the circuit can be classified as conductors, insulators, or resistors.

Using Ohm’s law equation V=IR, the current flowing through the circuit can be calculated. Ohm’s law is applied in circuits where the equivalent resistance and voltage applied are known. Based on the calculated current value, the conductor size and component current rating can be selected. The power loss of the circuit, otherwise called Joule heating loss, can be evaluated using the calculated current.

## Kirchhoff’s Laws

Kirchhoff’s laws are two basic, essential laws needed to perform electrical circuit network analysis. The two laws are Kirchoff’s current law and Kirchoff’s voltage law.

### Kirchhoff’s Current Law (KCL)

According to Kirchhoff’s current law, the algebraic sum of currents meeting at a junction in an electric circuit is zero. The law can be otherwise stated as the sum of incoming currents at a junction in an electric circuit is equal to the sum of outgoing currents. KCL is also called Kirchhoff’s junction, or nodal rule. KCL is based on the law of conservation of charge.

### Kirchhoff’s Voltage Law (KVL)

According to Kirchhoff’s voltage law, in a closed mesh, the algebraic sum of potential differences or voltages is zero. In a resistive electric current, KVL can be defined as the algebraic sum of voltage drops that access the resistors and voltage sources equal to zero. By using KVL, the current flowing through any closed loop can be calculated, provided the component value and voltage sources are known.

## Nodal Analysis and Mesh Analysis

Nodal analysis is the method used in circuit analysis to determine the voltages at nodes in a circuit. Nodes are the meeting point of two or more components. The voltage at the nodes can be calculated in terms of branch currents using nodal analysis. KCL governs nodal analysis.

Mesh analysis is the method used in circuit analysis to determine the current flowing in closed loops present in the circuit. When you have to solve the circuit without a calculator, using mesh analysis is best. It forms simultaneous equations with unknown variables and the solution gives the current values in each mesh. Mesh analysis is governed by Kirchhoff’s voltage law and is suitable only for planar circuits or networks.

## Theorems Used for Electrical Circuit Network Analysis

There are various theorems used to simplify circuit analysis:

1. Superposition Theorem

2. Thevenin’s Theorem

3. Norton’s Theorem

Understanding basic quantities such as voltage, current, resistance, power, inductor, capacitors, fundamental laws, and theorems simplifies the process of electrical circuit network analysis.

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