CBSE Class 12-science Answered
Calculate the capacitance of the following multi slab capacitor.
![question image](http://images.topperlearning.com/topper/new-ate/393454IMG20210521190329.jpg)
Asked by hitanshu04 | 21 May, 2021, 19:05: PM
Let σ be the surface charge density on capacitor plates .
If a dielctric slab of dielectric constant K and thickness d is inside capacitor plates ,
Then electric field E in the dielectric slab is given as
![begin mathsize 14px style E space equals space fraction numerator sigma over denominator K space epsilon subscript o end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/ba66323c1ac97e2cd3ce484aa0e84cc0.png)
Potential difference across dielectric slab, V = E × d =
........................(2)
![begin mathsize 14px style fraction numerator sigma over denominator K space epsilon subscript o end fraction cross times d end style](https://images.topperlearning.com/topper/tinymce/cache/dbf5658597308fc5991048b2333633f2.png)
Potential difference across capacitor plates having three different dielectric slabs is given as
![begin mathsize 14px style V space equals space V subscript 1 space plus space V subscript 2 space plus space V subscript 3 space end subscript space equals space fraction numerator sigma over denominator K subscript 1 space epsilon subscript o end fraction cross times d subscript 1 space plus space space fraction numerator sigma over denominator K subscript 2 space epsilon subscript o end fraction cross times d subscript 2 space plus space space fraction numerator sigma over denominator K subscript 3 space epsilon subscript o end fraction cross times d subscript 3 end style](https://images.topperlearning.com/topper/tinymce/cache/5b74eefb967772845326f44481311670.png)
If Q is the total charge on capacitor plates and A is area of plates , then surface charge density σ = ( Q / A )
By substituting surface charge density in eqn.(3) , we get
![begin mathsize 14px style V space equals space Q over A space open parentheses fraction numerator d subscript 1 over denominator K subscript 1 space epsilon subscript o end fraction space plus space space fraction numerator d subscript 2 over denominator K subscript 2 space epsilon subscript o end fraction space plus space space fraction numerator d subscript 3 over denominator K subscript 3 space epsilon subscript o end fraction close parentheses end style](https://images.topperlearning.com/topper/tinymce/cache/49bb470d45d6867075f6bbe04a227ed1.png)
Using the definition of capacitance C = ( Q / V ) , we get capacitance of multislab dielectric capacitor as
![begin mathsize 14px style C thin space equals space Q over V space equals space fraction numerator A space epsilon subscript o space over denominator open parentheses fraction numerator d subscript 1 over denominator K subscript 1 space end fraction space plus space space fraction numerator d subscript 2 over denominator K subscript 2 space end fraction space plus space space fraction numerator d subscript 3 over denominator K subscript 3 space end fraction close parentheses end fraction space end style](https://images.topperlearning.com/topper/tinymce/cache/4014631917c8805914c77c9ff6fefa0c.png)
Answered by Thiyagarajan K | 21 May, 2021, 20:55: PM
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