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CBSE Class 12-science Answered

Find the current supplied by the 7 volts source in the circuit shown in the following figure
question image
Asked by nikhilsai2616 | 19 Nov, 2023, 01:05: AM
answered-by-expert Expert Answer
Figure shows the current distribution in the given circuit.
 
Potential difference between A and E is 7 V . Hence , we have
 
begin mathsize 14px style 3 space i subscript 2 space plus space i subscript 5 space end subscript plus space left parenthesis space 5 space V space right parenthesis space equals space 7 space V end style
begin mathsize 14px style 3 space i subscript 2 space plus space i subscript 5 space end subscript space equals space 2 space V end style  ........................ (1)
 
Let us apply Kirchoff's voltage law to the loop ABCFA, then we get
 
begin mathsize 14px style 5 space i subscript 3 space plus space 3 space i subscript 4 space minus space 3 space i subscript 2 space equals space 0 end style  ............................(2)
 
Let us apply Kirchoff's voltage law to the loop FCDEF, then we get
 
begin mathsize 14px style i subscript 5 space plus space left parenthesis space 5 space V space right parenthesis space plus space 6 space i subscript 5 space plus space 3 space i subscript 4 subscript space end subscript space equals space 0 end style
 
begin mathsize 14px style negative 7 space i subscript 5 space end subscript minus space 3 space i subscript 4 space equals space 5 space V end style  ...............................(3)
 
If we apply Kirchoff's current law to node F, we get
 
begin mathsize 14px style i subscript 5 space equals space i subscript 2 space plus space i subscript 4 end style  ...........................(4)
 
By substituting begin mathsize 14px style i subscript 2 end style from eqn.(4) , we rewrite eqn.(1) as
begin mathsize 14px style 4 space i subscript 5 space minus space 3 space i subscript 4 space equals space 2 end style V ......................(4)
 
From eqn.(3) and eqn.(4), we get , begin mathsize 14px style i subscript 5 space equals negative space 3 over 11 space A space space a n d space space i subscript 4 subscript space end subscript space equals negative space 34 over 33 space A end style
By substituting begin mathsize 14px style i subscript 5 subscript space end subscript space a n d space i subscript 4 end style in eqn.(4) , we get begin mathsize 14px style i subscript 2 equals space 25 over 33 space A end style
By substituting begin mathsize 14px style i subscript 2 end style and begin mathsize 14px style i subscript 4 end style in eqn.(2) , we get begin mathsize 14px style i subscript 3 space equals space 59 over 55 space A end style
 
If we apply Kirchoff's current law to node A , we get
 
begin mathsize 14px style i subscript 1 space equals space i subscript 2 space plus space i subscript 3 space equals space open parentheses 25 over 33 plus 59 over 55 close parentheses space A space space equals space 302 over 165 A space equals space 1.830 space A end style
Hece current delivered by 7 V battery is 1.830 A
 
 



Answered by Thiyagarajan K | 19 Nov, 2023, 07:31: AM

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