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What is the value of R

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Asked by Prashant DIGHE 22nd July 2019, 3:45 PM
Answered by Expert
Answer:
Let current i drawn from 10 V battery is getting divided as i1 and i2  as shown in figure.
Current i1 is passing through 4V battery and current i2 is passing through 6V battery as shown in figure.
 
Let us apply Kirchoff's voltage law to the loop A-B-C-D-A :-   10 -2i -R i1 -4 = 0   or 2i + R i1 = 6  ................ (1)
 
since we have,  i = i1 + i2 ,  eqn.(1) is rewritten as,  (R+2) i1 + 2 i2 = 6  ....................... (2)
 
Let us apply Kirchoffs voltage law to the loop A-B-E-F-A :- 10 - 2i - 4 i2 -6 = 0   or i + 2 i2 = 2
 
since we have,  i = i1 + i2 ,  eqn.(1) is rewritten as,   i1 + 3 i2 = 2  ....................... (3)
 
if i2 = 0 , then from eqn.(3),  i1 = 2 A  
 
if we substitute, i2 = 0 and i1 = 2 A  in eqn.(2), we get R = 1 Ω
Answered by Expert 22nd July 2019, 7:12 PM
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