CBSE Class 12-science Answered
Find the current in each branch of the circuit.
![question image](http://images.topperlearning.com/topper/new-ate/647611IMG20210708WA0002.jpg)
Asked by hitanshu92 | 09 Jul, 2021, 22:22: PM
By applying Kirchoff's voltage law to the top loop ' acdba ' , we get
-2
2 - 4 + 3
1 = 10 or 3
1 - 2
2 = 14 ............................. (1)
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
By applying Kirchoff's voltage law to the top loop ' cefdc ' , we get
-
3 - 3
1 = - 4 or 3
1 +
3 = 4 .............................(2)
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
At node d , if we apply Kirchoff's Current law , we get
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
By substituting
3 using eqn. (3) , we rewrite eqn.(2) as
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
4
1 +
2 = 4 ..................................(4)
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
By solving eqn.(1) and eqn.(3) , we get ,
1 = 2 A and
2 = -4 A
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
From eqn.(3) , by substituting
1 and
2 , we get
3 = -2 A
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
Answered by Thiyagarajan K | 10 Jul, 2021, 00:37: AM
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