# Solved Problems-15

Problems-15

An e.m.f. source

*E*, having negligible internal impedance is connected in series with an impedance*Z*_{1}to the input terminals 1â€“2 of a linear, bilateral four terminal network. It produces a current*I*_{2}in impedance*Z*connected across the output terminals 3â€“4. The emf source is now transferred so as to act, in series with_{L}*Z*_{2}, between terminal 3â€“4.*Z*_{1}is disconnected and the input terminals 1â€“2 are short circuited. The short-circuited current traversing terminals 1â€“2 is then*I*_{1}. Prove that the impedance looking into terminals 1â€“2 under the first condition is,Solution

Let the impedance looking into terminals 1â€“2 be

*Z*_{12}.Thus the network becomes:

âˆ´

âˆ´ Voltage across 1â€“2,

So, the circuit becomes as shown.

The given network is linear and bilateral and according to the reciprocity theorem, if the source

*E*is put across terminals 1â€“2, the response current flowing through*Z*_{2}will be*I*_{1}as shown.Now, if a voltage equal to

*V*_{12}is applied instead of*E*, the current flowing through*Z*_{2}will be,But, this current is equal to

*I*_{2}.âˆ´

â‡’ (Proved)