Star - Delta transformation

A star network can be transformed to its equivalent delta connection and a delta can be transformed to its equivalent star connection. The star-delta transformation is

Current Division

The Current Divider Rule

Current divider rule is used to find the current passing through an element connected in a parallel network.

If there are N resistors R₁, R₂,..….R_N; connected in parallel with a source delivering a total current, I_T to the circuit as shown in the below figure. Then the current through i th resistor

Parallel Connection in Circuits

If the elements or components of a network are connected in parallel then the voltage across all the elements are equal but the current may vary from element to element. The parallel circuit has more than one path to the flow of current. Most of the equipment in the power system is connected in parallel. Unlike a series circuit an open circuit at one of the elements doesn't

Voltage Division Formula and Derivation

Voltage Divider Rule

Voltage divider rule is used to find the voltage across an element connected in a series network.

If there are N resistors R₁, R₂,..….R_N; connected in series with a voltage source of voltage V_S as shown in the below figure. Then the voltage across i th resistor is,

Maximum Power Transfer theorem

Maximum Power Transfer theorem for DC excitation

Statement

A linear DC network having a resistive load connected receives maximum power when the load resistance is

Tellegen’s theorem

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Tellegen’s theorem statement

The Tellenen’s theorem states that the algebraic sum of powers in a network is zero. Where the powers delivered by the active elements are taken as negative and the power consumed at the passive elements is taken as positive or vice versa. Alternatively it can be explained as

Source Transformation of Voltage source and Current source

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Source Transformation

In the analysis of electrical circuits it is often necessary to transform a voltage source to current source or a current source to voltage source for simplifying circuit the calculations. For applying source transformation it is necessary that the voltage source mush have a resistance in series with it (practical voltage source) and a current source must have resistance in parallel with it (practical current source). The source transformation cannot be performed

Millman’s Theorem

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Millman’s Theorem statement

The millman’s theorem states that, when a circuit has n number of voltage sources such as V₁, V₂, V₃⋅⋅⋅⋅⋅⋅⋅V_n along with their internal resistances R₁, R₂, R₃, ⋅⋅⋅⋅⋅⋅⋅R_n respectively are connected in parallel as shown in the below figure, then the circuit can be replaced by a single

Reciprocity theorem

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Reciprocity Theorem Statement

Reciprocity theorem states that, for a network consisting of linear, bilateral elements, the ratio of excitation to response at an element due to a single excitation (source) is constant, even when the positions of

Resistor Color Coding

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Resistors use various color bands to specify their values. These color bands are used instead of numbers due to their simplicity and cost effective printing on tiny components.

The following table lists the various color codes

Instantaneous value

Instantaneous value of a time varying wave form

The value of a time varying quantity such as alternating current is not constant and varies with respect to time. The value of such a quantity at an instant of time is called

Resonance in electrical circuits

Electrical Resonance

In electrical circuits resonance is a phenomenon when the voltage and current are in phase with is each other. That is, the phase angle between the voltage and the current is zero. In circuits with pure resistive elements doesn't have

Super position Theorem

Statement

Super position Theorem states that the voltage across (or current through) an element in a linear circuit is equal to the algebraic sum of voltages across (or currents through) that element due to each independent source acting alone.

Alternatively it can be explained as; in a circuit having multiple number of sources, which are turned on simultaneously. The response (voltage or current) obtained

Norton’s Theorem

Norton’s Theorem statement

Statement for DC

Norton’s theorem states that any two terminal linear network having number of voltage sources, current sources and resistances can be replaced by a simple equivalent circuit consisting of a single current source, I_N in parallel with a resistance R_N. Whereas the value of the current source, I_N is the short circuit

Thevenin’s Theorem

Thevenin’s Theorem statement:

Statement for DC

Thevenin’s theorem states that any two terminal linear network having number of voltage sources, current sources and resistances can be replaced by a simple equivalent circuit consisting of a single voltage source, V_th in series with a resistance R_th. Whereas the value of the voltage source, V_th is the

Electrical Energy Sources and Their Classification

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Energy Sources

Energy sources are the active elements which supply electrical energy to the circuits.

Classification of Energy Sources

Energy sources are classified into two types as independent and dependent sources. The independent sources are further divided into two types namely voltage source and the voltage source. There are four types of the dependent sources. They are

Inductance / Inductor

Inductance

Inductance or Inductor indicated by letter ‘L’ is a passive circuit element that stores energy in the form of magnetic field. Inductors are the coils generally wounded over a permeable medium. The windings in electrical machines and transformers

Voltage Source

A voltage source is an active element in electrical circuits which delivers voltage to the circuit. An ideal voltage source should have no internal resistance (or Impedance in AC) and its output voltage is independent of the current passing through the element. The voltage delivered by an ideal voltage source is always

Practical Current source

Practically the current sources don’t have infinite resistance across them but has some finite and high resistance. Due to the finite resistance the practical current source shows some dependency on the voltage across it. So the current delivered by a practical current

Delta connection

The Delta connection (or ∆ - connection) is a type of circuit configuration in electrical circuits. If the three elements of a circuit viz. aa’, bb’ and cc’ are connected in such a way that their ends a’ is connected to b, b’ to c and c’ to a to from a triangle then such a network is said to be a delta connected network. The given below figure shows a delta