# Circuit Analysis Theorems

## Circuit Analysis Theorems:

Principle of Superposition Theorem : The Principle of Superposition Theorem states that in any linear network containing two or more sources, the response in any element is equal to the algebraic sum of the responses caused by individual sources acting alone, while the other sources are non-operative; that is, while considering the effect of individual sources, other ideal voltage sources and ideal current sources in the network are replaced by short circuit and open circuit across their terminals. This theorem is valid only for linear systems. This theorem can be better understood with a numerical example. Consider the Circuit Analysis Theorems which contains two sources as shown in Fig. 3.7. Now let us find the current passing through the 3 Ω resistor in the circuit. According to Principle of Superposition Theorem, the current /2 due to the 20 V Voltage source with 5 A source open …

Star Delta Control Circuit : The star delta transformation is another technique useful in solving complex networks. Basically, any three circuit elements, i.e. resistive, inductive or capacitive, may be connected in two different ways. One way of connecting these elements is called the star connection, or the Y connection. The other way of connecting these elements is called the delta (Δ) connection. The circuit is said to be in Star Delta Control Circuit, if three elements are connected as shown in Fig. 3.1(a), when it appears like a star (Y). Similarly, the circuit is said to be in delta connection, if three elements are connected as shown in Fig. 3.1(b), when it appears like a delta (Δ). The above two circuits are equal if their respective resistances from the terminals AB, BC and CA are equal. Consider the Star Delta Control Circuit in …

Thevenin Equivalent Circuit : In many practical applications, it is always not necessary to analyse the complete circuit; it requires that the voltage, current, or power in only one resistance of a circuit be found. The use of this theorem provides a simple, equivalent circuit which can be substituted for the original network. Thevenin Equivalent Circuit states that any two terminal linear network having a number of voltage current sources and resistances can be replaced by a simple equivalent circuit consisting of a single voltage source in series with a resistance, where the value of the voltage source is equal to the open circuit voltage across the two terminals of the network, and resistance is equal to the equivalent resistance measured between the terminals with all the energy sources are replaced by their internal resistances. Circuit Analysis Theorems …