Find the current in each branch of the circuit. 

Asked by hitanshu92 | 9th Jul, 2021, 10:22: PM

Expert Answer:

By applying Kirchoff's voltage law to the top loop ' acdba ' , we get
 
-2 begin mathsize 14px style straight I end style2 - 4 + 3 begin mathsize 14px style straight I end style1 = 10     or  3 begin mathsize 14px style straight I end style1 - 2 begin mathsize 14px style straight I end style2 = 14  ............................. (1)
 
By applying Kirchoff's voltage law to the top loop ' cefdc ' , we get
 
begin mathsize 14px style straight I end style3 - 3 begin mathsize 14px style straight I end style1 = - 4      or   3 begin mathsize 14px style straight I end style1 + begin mathsize 14px style straight I end style3 = 4 .............................(2)
 
At node d , if we apply Kirchoff's Current law , we get
 
begin mathsize 14px style straight I end style1 + begin mathsize 14px style straight I end style2 = begin mathsize 14px style straight I end style3  ....................................(3)
 By substituting begin mathsize 14px style straight I end style3 using eqn. (3) , we rewrite eqn.(2) as 
begin mathsize 14px style straight I end style1 + begin mathsize 14px style straight I end style2 = 4  ..................................(4)
 
By solving eqn.(1) and eqn.(3) , we get , begin mathsize 14px style straight I end style1 = 2 A   and begin mathsize 14px style straight I end style2 = -4 A  
From eqn.(3) , by substituting begin mathsize 14px style straight I end style1 and begin mathsize 14px style straight I end style2 , we get  begin mathsize 14px style straight I end style3 = -2 A

Answered by Thiyagarajan K | 10th Jul, 2021, 12:37: AM