3946 Views

derive an expression for the energy stored in a capacitor with Air as the medium between its plates.how does the stored energy change if Air is replaced by a medium of dielectric constant k


byabangtaking19 25th Oct, 2020
Answer (1)
gauravvijayvargiya399 26th Oct, 2020

Let us consider a capacitor of capacitance C and potential difference V between the plates.

Let the charge on one plate be +q and -q on the other.

Suppose the capacitor is being charged gradually.

Now,at any stage the charge on capacitor is q.

Therefore, the potential difference =  q/C

Small amount of work done in giving n additional charge dq to the capacitor is =

dW = C/q × dq

Total work done in giving a charge Q to the capacitor  is

W=∫dW  ~~~~~~ (A) equation

Now, by putting the value of dW = C/q × dq in above equation (A) and integrating it and putting values of upper limit = Q and lower limit = 0 and thus integrating the whole equation we get,

W = Q^2/ C

Here let Energy= E

E= Q^2/ 2C

= C V^2 / 2

= QV/2

The energy is stored in the form of potential energy.

Hope that helps

Related Questions

UPES Integrated LLB Admission...
Apply
Ranked #28 amongst Institutions in India by NIRF | Ranked #1 in India for Academic Reputation by QS University Rankings | 16.6 LPA Highest CTC
Jindal Global Law School Admi...
Apply
Ranked #1 Law School in India & South Asia by QS- World University Rankings | Merit cum means scholarships | Application Deadline: 30th Nov'24
Chandigarh University Admissi...
Apply
Ranked #1 Among all Private Indian Universities In QS Asia Rankings 2025 | Scholarships worth 210 CR
Great Lakes PGPM & PGDM 2025
Apply
Admissions Open | Globally Recognized by AACSB (US) & AMBA (UK) | 17.3 LPA Avg. CTC for PGPM 2024 | Application Deadline: 1st Dec 2024
ICFAI Business School-IBSAT 2024
Apply
9 IBS Campuses | Scholarships Worth Rs 10 CR
Nirma University Law Admissio...
Apply
Grade 'A+' accredited by NAAC
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books