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Reciprocity Theorem

According to this theorem if the source of voltage and zero-resistance ammeter are interchanged, the magnitude of the current through the ammeter will  be the same, no matter how complicated the network is, Indeed this principle states that the directional characteristics of a receiving antenna are the same as the directional characteristics of the same antenna when used for transmission. This is a highly useful relation.

In other words supply voltage V and current I are mutually transferable. The ratio of V and I is called the transfer resistance (or transfer impedance).

Q. Determine the reading of the ammeter (i) when it is connected in the arm CD and battery in arm AF and (ii) when the battery is in arm CD an diameter in arm AF of the circuit shown in. Also determine the value of transfer resistance.

Solution: Equivalent resistance of the network shown in.

R' = 2+ 8+  1   =15Ω
            1 + 1
           10  5+5

current supplied by battery

I' = 30 =2A

Ammeter current,  I' 2 = 2 X 10  =1 A

Equivalent resistance of the network shown in.

R" = 5+ 5 +  1  = 15Ω
                1 + 1
              10  2+8

Current supplied by the cattery,

I" = 30 = 30  =2A
      R"    15

Ammeter current, I2" = 2 X    10   =1 A

Hence ammeter reading in both cases in the same

Transfer resistance = 30 = 30Ω

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