Network theorems

Network theorems:

    1) Thevenin’s theorem: This theorem is developed by the French engineer M.L.Thevenin to reduce the whole circuit to an equivalent circuit with single voltage sources and series resistance according to his name this theorem is known as Thevenin’s theorem. This theorem is possibly the mostly used theorem it is applicable where it is desired to determine current through or voltage across any one network element without going through the rigorous method of solving set of network equation.

Statement: “any linear active network consisting of independent or dependent voltage and current and linear bilateral element can be replaced by an equivalent circuit consisting of voltage source in series with a resistance, voltage source being the open circuited and voltage across the open circuited load terminals and resistance being the internal resistance of the source network looking through the open circuited load terminal”

   2) Norton’s theorem: Norton theorem is converse of Thevenin’s theorem. It consists of equivalent current source instead of equivalent voltage source as we do it in Thevenin’s theorem. The determination of internal resistance of the source network is identical in both the theorem. However, in final stage, in Norton resistance unlike to that in Thevenin’s theorem where the equivalent voltage source was placed in series with the internal resistance.

Statement: “a liner active network consists of independent and dependent voltage and current and liner bilateral network elements can be replaced by an equivalent circuit, consisting of a current source in parallel with a resistance. The current source being the short-circuited current across the load terminal and the resistance being the internal resistance of the source network, looking through the open circuited load”

   3) Superposition theorem: “The total current in any part of a linear circuit equals the algebraic sum of the currents produced by each source separately. The superposition theorem is an important concept in circuit analysis. It allows you to determine a voltage across a component or a branch current by calculating the effect of each source individually, then algebraically adding each contribution.”

    4) Reciprocity theorem: In any branch of a network or circuit, the current due to a single source of voltage (V) in the network is equal to the current through that branch in which the source was originally placed when the source is again put in the branch in which the current was originally obtained. This theorem is used in the bilateral linear network which consists bilateral components.

    5) Maximum power transfer theorem: The maximum power transfer theorem states that in a linear, bilateral DC network, maximum power is delivered to the load when the load resistance is equal to the internal resistance of a source. If it is an independent voltage source, then its series resistance (internal resistance) or if it is independent current source, then its parallel resistance (internal resistance) must equal to the load resistance to deliver maximum power to the load.