The ratio of true power to apparent power in an AC Circuit is called the power factor and can be expressed as follows: \[PF=\frac{True\text{ Power P}}{Apparent\text{ Power S}}\] It is also defined as the ratio of resistance to the impedance (series circuit): \[PF=\frac{\operatorname{Resistance}\text{ R}}{\operatorname{Impedance}\text{ Z}}\] Since R/Z is the …

Read More »## Apparent, Active and Reactive Power

This section covers basic concepts about apparent, active (real) and reactive power which is important ingredients in the analysis of a power system. Consider the general single-phase circuit with a sinusoidal voltage $v={{V}_{m}}sin\left( wt \right)$ applied. A current $i={{I}_{m}}sin(wt\pm \theta )$ results and is leading (θ is positive) for a capacitive …

Read More »## Maximum Power Transfer Theorem

Maximum Power Transfer Theorem Definition Maximum power transfer theorem states that maximum power output is obtained when the load resistance RL is equal to Thevenin resistance Rth as seen from load Terminals. Fig.1: Maximum Power Transfer Theorem Any circuit or network may be represented by a Thevenin equivalent circuit. The Thevenin …

Read More »## Nodal Analysis or Node voltage Method

Nodal analysis or Node voltage method uses node voltages as circuit variables in order to analyze the circuit. The objective of this section is to obtain a set of simultaneous linear equations. However, unlike the mesh analysis method, the procedure developed in this section depends on the choice of certain …

Read More »## Mesh Current Analysis | Mesh Analysis

The mesh is a closed path which does not contain any other closed path within it. This section shows that a set of simultaneous linear equations can be written which describes the network. This set of equations depends on a choice of loop currents used in connection with Kirchhoff’s law. …

Read More »## Kirchhoff’s Voltage Law (KVL)

In order to present Kirchhoff’s voltage law, we must introduce the concept of a “loop”. Since energy must be conserved when a charge goes around a loop, the energy given up by the charge equals the energy it gains. The same energy-conservation principle would apply if you carried a rock …

Read More »## Kirchhoff’s Current law (KCL)

For a given circuit, a connection of two or more elements is called a NODE. The particular circuit shown in figure 1 depicts an example of a node. Figure.1: Circuit for Kirchhoff’s Current Law We now present the Kirchhoff’s current law which is essentially the law of conservation of electric …

Read More »## RC Series Circuit Analysis | RC Time Constant

In the case of a resistive-capacitive (RC) series circuit, when the supply is first switched on the charging current is initially at its maximum level, then it gradually falls to zero. The capacitor voltage is zero at first and grows gradually to its maximum level. As with the RL Circuit, …

Read More »## Resistors in Series and Parallel

Resistance Resistance is defined as the measure of opposition to the motion of electrons due to their continuous collisions, with the atoms of the conductor. The unit of resistance is ohm. Let’s consider the conductor of cross-sectional area A and of length L as given below: The resistance of this …

Read More »## Capacitors in Series and Capacitors in Parallel

A capacitor is a passive device which stores energy in an electric field and opposes the change in voltage. An electric field can be created by placing two conducting plates in parallel and having one plate more positive than other as shown in fig. The material between two plates is …

Read More »## RL Series Circuit Analysis

When a resistive-inductive (RL) series circuit has its supply voltage switched on, the inductance produces an initial maximum level of counter-emf that gradually falls to zero. The circuit current is zero initially and grows gradually to its maximum level. The behavior of an RL series circuit is most easily understood …

Read More »## Inductors in Series and Parallel | Energy Stored in Inductor

In this section, we will calculate an equivalent inductance of inductors in series and inductors in parallel. Inductors in Series The method for determining the total inductance of the following circuit is similar to that used for series resistors. According to Kirchhoff’s voltage law, we can write following equation for the …

Read More »## Mutual Inductance and Self Inductance | Formula & Example

Electromagnetic induction occurs when a magnetic flux in motion with respect to a single conductor or a coil induces an emf in the conductor or coil. Because the growth or decline of current through a coil generates a changing flux, an emf is induced in the coil by its own …

Read More »## Superposition Theorem

Superposition theorem is stated as follows: The current is any circuit element or voltage across any element of a linear bilateral network is the algebraic sum of the currents or voltages separately produced by each source of energy. Simultaneous equations may be avoided in the solution of a complex network …

Read More »## Norton’s Theorem | Norton’s Equivalent Circuit

Norton’s Theorem states that: Suppose we are given an arbitrary circuit containing any or all of the following elements: resistors, voltage sources, current sources (the source can be dependent as well as independent). Let us identify a pair of nodes, say node a and b, such that the circuit can …

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