15 February, 2007

Reciprocity Theorem

In its simplest form, the reciprocity theorem states that if an emf E in one branch of a reciprocal network produces a current I in another, then if the emf E is moved from the first to the second branch, it will cause the same current in the first branch, where the emf has been replaced by a short circuit. We shall see that any network composed of linear, bilateral elements (such as R, L and C) is reciprocal.

It is sometimes phrased as the statement that voltages and currents at different points in the network can be interchanged. More technically, it follows that the mutual impedance of a first circuit due to a second is the same as the mutual impedance of the second circuit due to the first.

The circuit in the figure is a concrete example of reciprocity. The reader should solve the circuit, and determine the values of the current I in the two cases, which will be equal (0.35294 A). If E is reversed, then the direction of I is reversed, so the direction does not matter so long as both E and I are reversed at the same time.

Note : A non-bilateral element, such as a rectifying diode, destroys reciprocity.A nonlinear element also destroys reciprocity.

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1 comment:

Anonymous said...

all the components must be passive too. a voltage or current source(dependant or not) in the network detroys its reciprocity.