(a) Derive an expression for the energy stored in a parallel plate capacitor of capacitance C when charged up to voltage V. How is this energy stored in the capacitor ?

(b) A capacitor of capacitance 1 \mu F is charged by connecting a battery of negligible internal resistance and emf 10 V across it. Calculate the amount of charge supplied by the battery in charging the capacitor fully.

 

 
 
 
 
 

Answers (1)
S safeer

a) 

Let the charge on the capacitor is increased by dq amount then,

Then, the work done:-

dU=Vd{Q}'=\frac{{Q}'}{C}\; d{Q}'

On integrating it, we have

\int_{O}^{U}dU=\frac{1}{C}\int_{O}^{Q}{Q}'d\;{Q}'

U=\frac{1}{2}\left [ \frac{Q^{2}}{C} \right ]^{Q}_{O}

U=\frac{1}{2}\frac{Q^{2}}{C}

We know, C=\frac{Q}{V}

            U=\frac{1}{2}CV^{2}

            U=\frac{1}{2}QV

\therefore This is the work done is stored as energy on the capacitor 

The electrostatic Energy energy is stored in the electric field between the plates.

b)

\\Q=CV\\Q=1\times10^{-6}\times10=10\mu C

Preparation Products

Knockout NEET May 2023 (Easy Installments)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 5499/-
Buy Now
Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout NEET Aug 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Knockout NEET Aug 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions