Capacitor A is charged by a 120 V battery and capacitor B is charged by 100 V battery. If the energy stored in both the capacitors is the same then find the ratio of the capacitance of capacitor A to capacitor B.

  1. 36 : 25
  2. 25 : 36
  3. 5 : 6
  4. None of these

Answer (Detailed Solution Below)

Option 2 : 25 : 36
Free
CRPF Head Constable & ASI Steno (Final Revision): Mini Mock Test
21 K Users
40 Questions 40 Marks 45 Mins

Detailed Solution

Download Solution PDF

CONCEPT:

Capacitor:

  • The capacitor is a device in which electrical energy can be stored.
    • In a capacitor two conducting plates are connected parallel to each other and carrying charges of equal magnitudes and opposite signs and separated by an insulating medium.
    • The space between the two plates can either be a vacuum or an electric insulator such as glass, paper, air, or a semi-conductor called a dielectric.

Capacitance:

  • The property to store energy in form of charge is called capacitance.
  • The unit of capacitance is Farad.
  • The charge on the capacitor (Q) is directly proportional to the potential difference (V) between the plates,

​⇒ Q ∝ V

⇒ Q =  CV

Where C = capacitance

Energy stored in the capacitor:

  • If a capacitor of capacitance C is charged by a potential difference V, then the energy stored in the capacitor is given as,

\(\Rightarrow U=\frac{1}{2}CV^2=\frac{Q^2}{2C}\)

CALCULATION:

Given VA = 120 V, VB = 100 V, and UA = UB

  • We know that if a capacitor of capacitance C is charged by a potential difference V, then the energy stored in the capacitor is given as,

\(\Rightarrow U=\frac{1}{2}CV^2\)       ----(1)

By equation 1 for the capacitor A,

\(\Rightarrow U_A=\frac{1}{2}C_AV_A^2\)       ----(2)

By equation 1 for the capacitor B,

\(\Rightarrow U_B=\frac{1}{2}C_BV_B^2\)       ----(3)

By equation 2 and equation 3,

∵ UA = UB

\(\Rightarrow \frac{1}{2}C_AV_A^2=\frac{1}{2}C_BV_B^2\)

\(\Rightarrow \frac{C_A}{C_B}=\frac{V_B^2}{V_A^2}\)

\(\Rightarrow \frac{C_A}{C_B}=\frac{100^2}{120^2}\)

\(\Rightarrow \frac{C_A}{C_B}=\frac{25}{36}\)

Hence option 2 is correct.

Latest Indian Coast Guard Navik GD Updates

Last updated on Jul 4, 2025

-> The Indian Coast Guard Navik GD Application Correction Window is open now. Candidates can make the changes in the Application Forms through the link provided on the official website of the Indian Navy.

-> A total of 260 vacancies have been released through the Coast Guard Enrolled Personnel Test (CGEPT) for the 01/2026 and 02/2026 batch.

-> Candidates can apply online from 11th to 25th June 2025.

-> Candidates who have completed their 10+2 with Maths and Physics are eligible for this post. 

-> Candidates must go through the Indian Coast Guard Navik GD previous year papers.

More Energy Stored in an Electric Field Questions

More Capacitance Questions

Get Free Access Now
Hot Links: online teen patti real money master teen patti teen patti master old version teen patti chart