Answer
406.2k+ views
Hint: In this question, we will first calculate the charge induced across the plates of the capacitor. When the distance between the plates is halved, the capacitance will increase by two times too.
Complete step by step answer
We know that the capacitance of a capacitor is given as
$ C= \dfrac {\epsilon A}{d} $
where $ A $ is the area of the capacitor and $ d $ is the distance between the plates of the capacitor.
So, we can see that when the distance between the plates of the capacitor is halved, the capacitance will increase to twice as $ C \propto \dfrac{1}{d} $ . If we indicate the new capacitance by $ C' $ ,
$ \dfrac{{C'}}{C} = \dfrac{d}{{d/2}} = \dfrac{2}{1} $
So, we can write
$ C' = 2C $
Now, the charge of a capacitor is given as
$ Q = CV $
Since the capacitance doubles up, the charge across the plates $ Q' $ in the new situation will also double up. So $ Q' = 2Q = 2CV $ .
The work done by the battery when the charge across the capacitor will double will be
$ W = \Delta QV $
Since $ \Delta Q = Q' - Q $
$ \Rightarrow \Delta Q = 2CV - CV = CV $ ,
The work done will be
$ W = \left( {CV} \right)V $
$ \Rightarrow W = C{V^2} $
Hence the correct choice will be option (D).
Note
Since the battery will remain connected to the capacitor plates, the potential across the capacitor will also remain constant. Hence the change in charge stored by the capacitor will only be due to the change in the capacitance due to a change in the distance between the plates. In the process, the battery will do work on the capacitor to provide more energy to the capacitor.
Complete step by step answer
We know that the capacitance of a capacitor is given as
$ C= \dfrac {\epsilon A}{d} $
where $ A $ is the area of the capacitor and $ d $ is the distance between the plates of the capacitor.
So, we can see that when the distance between the plates of the capacitor is halved, the capacitance will increase to twice as $ C \propto \dfrac{1}{d} $ . If we indicate the new capacitance by $ C' $ ,
$ \dfrac{{C'}}{C} = \dfrac{d}{{d/2}} = \dfrac{2}{1} $
So, we can write
$ C' = 2C $
Now, the charge of a capacitor is given as
$ Q = CV $
Since the capacitance doubles up, the charge across the plates $ Q' $ in the new situation will also double up. So $ Q' = 2Q = 2CV $ .
The work done by the battery when the charge across the capacitor will double will be
$ W = \Delta QV $
Since $ \Delta Q = Q' - Q $
$ \Rightarrow \Delta Q = 2CV - CV = CV $ ,
The work done will be
$ W = \left( {CV} \right)V $
$ \Rightarrow W = C{V^2} $
Hence the correct choice will be option (D).
Note
Since the battery will remain connected to the capacitor plates, the potential across the capacitor will also remain constant. Hence the change in charge stored by the capacitor will only be due to the change in the capacitance due to a change in the distance between the plates. In the process, the battery will do work on the capacitor to provide more energy to the capacitor.
Recently Updated Pages
What are the figures of speech in the poem Wind class 11 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write down 5 differences between Ntype and Ptype s class 11 physics CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Two tankers contain 850 litres and 680 litres of petrol class 10 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What happens when eggshell is added to nitric acid class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why was Kamaraj called as Kingmaker class 10 social studies CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What makes elections in India democratic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which mountains are called the Blue Mountains 1 Nilgiri class 8 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How many crores make 10 million class 7 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What is BLO What is the full form of BLO class 8 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)