Find the current in each resistor 

Asked by najeeb.razvi | 9th Aug, 2021, 06:45: PM

Expert Answer:

 
In the given circuit R1 and R4 are in series .
Hence Equivalent resistance R7 = 4Ω replaces resistors R1 and R4 in the circuit shown above.
 
Similarly , in the given circuit, R3 and R5 are in parallel. 
Hence Equivalent resistance R6 = 4Ω replaces resistors R3 and R5 in the circuit shown above. 
 
Let us assume the current distribution as shown in figure.
 
If we apply Kirchoff's voltage law to the loop ABEFA , we get
 
begin mathsize 16px style i end style1 + 4 begin mathsize 16px style i end style3 + 2 = 2   or  begin mathsize 16px style i end style1 = - begin mathsize 16px style i end style3   ............................ (1)
If we apply Kirchoff's voltage law to the loop BCDEB , we get 
 
begin mathsize 16px style i end style1 + 4 begin mathsize 16px style i end style2 + 2 = 2   or  begin mathsize 16px style i end style1 = - begin mathsize 16px style i end style2  ...........................(2) 
At node B , if we apply Kirchoff's current law , we get  begin mathsize 16px style i end style1 begin mathsize 16px style i end style2 begin mathsize 16px style i end style3  ...............................(3)
From equations (1), (2) and (3) , we get , begin mathsize 16px style i end style1 = begin mathsize 16px style i end style2  = begin mathsize 16px style i end style3 = 0
Hence current through all resistors is zero

Answered by Thiyagarajan K | 9th Aug, 2021, 08:33: PM