CBSE Class 12-science Answered
Find the current supplied by the 7 volts source in the circuit shown in the following figure
![question image](http://images.topperlearning.com/topper/new-ate/top_mob170033615212312603214b7ae84f-2034-4e3f-9978-1e8998c5abd2.jpg)
Asked by nikhilsai2616 | 19 Nov, 2023, 01:05: AM
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/70b636ff872dab3a3b9beb189fc91a2c655957093daab2.25013592f1.png)
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](https://images.topperlearning.com/topper/tinymce/cache/215b1d20fe973f7527db2354e036466d.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/11f30f8e2f93928e491c47f06f5a0f66.png)
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](https://images.topperlearning.com/topper/tinymce/cache/6921150c6333c287f0ec87a3451e2f8b.png)
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](https://images.topperlearning.com/topper/tinymce/cache/36cbe2a747f47297d13e9c755e79138e.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/58c94d2990dd1ce3530a2c1a7a00ed27.png)
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](https://images.topperlearning.com/topper/tinymce/cache/76c9a4783e9e0b322cc09b84b13fd907.png)
By substituting
from eqn.(4) , we rewrite eqn.(1) as
![begin mathsize 14px style i subscript 2 end style](https://images.topperlearning.com/topper/tinymce/cache/6d97073769a5277c2e5691b85a8a58f4.png)
![begin mathsize 14px style 4 space i subscript 5 space minus space 3 space i subscript 4 space equals space 2 end style](https://images.topperlearning.com/topper/tinymce/cache/f52a49588aa0293b0fd08fec16a0e783.png)
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](https://images.topperlearning.com/topper/tinymce/cache/bc5db9fc89d1e4a625035f255473c7f9.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/bc5db9fc89d1e4a625035f255473c7f9.png)
By substituting
in eqn.(4) , we get ![begin mathsize 14px style i subscript 2 equals space 25 over 33 space A end style](https://images.topperlearning.com/topper/tinymce/cache/44edd2922926004f7d9f9ab687a9a686.png)
![begin mathsize 14px style i subscript 5 subscript space end subscript space a n d space i subscript 4 end style](https://images.topperlearning.com/topper/tinymce/cache/82e98c0fbc2b6138301f01190ad8a725.png)
![begin mathsize 14px style i subscript 2 equals space 25 over 33 space A end style](https://images.topperlearning.com/topper/tinymce/cache/44edd2922926004f7d9f9ab687a9a686.png)
By substituting
and
in eqn.(2) , we get ![begin mathsize 14px style i subscript 3 space equals space 59 over 55 space A end style](https://images.topperlearning.com/topper/tinymce/cache/a19b2c18a1f6b3dbd4182c0dd37cb43f.png)
![begin mathsize 14px style i subscript 2 end style](https://images.topperlearning.com/topper/tinymce/cache/6d97073769a5277c2e5691b85a8a58f4.png)
![begin mathsize 14px style i subscript 4 end style](https://images.topperlearning.com/topper/tinymce/cache/d2ceeda61a6ed6725f0614987e2d088e.png)
![begin mathsize 14px style i subscript 3 space equals space 59 over 55 space A end style](https://images.topperlearning.com/topper/tinymce/cache/a19b2c18a1f6b3dbd4182c0dd37cb43f.png)
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](https://images.topperlearning.com/topper/tinymce/cache/2c97d6b3d9533a90eb2ec3023248ce22.png)
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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