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Solved Problems-14

Problems-14
Verify the Reciprocity Theorem for the network shown in the figure using current source and a voltmeter. All the values are in ohm.
 
Description: 3366.png
 
Solution
Using a current source and a voltmeter,
 
Let, e1e2 be node voltages, v1 be the voltmeter reading.
 
Description: 3373.png
 
By KCL,
At node (1)  Description: 6550.png (i)
 
At node (2)  Description: 6559.png (ii)
 
At node (3) Description: 6565.png (iii)
 
 
From (ii)  Description: 6571.png
 Description: 6582.png
 Description: 6588.png
 
From (i)  Description: 6594.png
 Description: 6600.png(A)
 
Interchanging the positions of the current source and the voltmeter,
 
Now, let v2 be the voltmeter reading
 
Description: 3421.png
 
By KCL,
At node (1)  Description: 6606.png(iv)
 
At node (2)  Description: 6612.png
 Description: 6618.png
⇒ Description: 6624.png(v)
 
At node (3)  Description: 6630.png
 Description: 6636.png
 Description: 6642.png(B)
 
From equations (A) and (B), Reciprocity theorem is proved.
 




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