Thursday, 14 March 2013
RECIPROCITY THEOREM
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RECIPROCITY THEOREM
The theorem states that
The current I in any branch of a network, due to a single voltage source E anywhere else in the network, will equal the current through the branch in which the source was originally located if the source is placed in the branch in which the current I was originally measured.
The reciprocity theorem is
applicable only to single-source networks.It is, therefore, not a theorem
employed in the analysis of multisource networks
In other words, the location of the voltage source
and the resulting current may be interchanged without a change in current. The
theorem requires that the polarity of the voltage source have the same
correspondence with the direction of the branch current in each position.
RTH = [ (2 + 4)
|| 6 ] +12 = 15Ω
IS = 45 / 15 =3 A
By using current division
rule
I = 3 * 6 / 12 = 1.5A
I = 1.5A
Now we have to intercahnce E
and I
Since I is pointed downwards
in the given problem. so the positive terminal placed downwards when we
interchange.
Since E positive terminal
points upwards in the given problem, the current I also points upwards in above
diagram when we interchange
RT = (12|| 6) + 2
+ 4 = 10 Ω
IS = 45 /10 =4.5A
By using current division
rule
I = 4.5 * 6 / ( 12 + 6) = 1.5A
I = 1.5A
Since in both cases I are
equal reciprocity theorem is verified
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