A parallel plate capacitor of capacitance C is connected to a battery and is charged to a potential difference V . Another capacitor of capacitance 2 C is similarly charge to a potential difference 2 V . The charging

Correct answer: B. (3)/(2) CV^ 2 From the figure. The net charge shared between the capacitors Q^ =Q_ 2 -Q_ 2 =4 C V-C V=3 C V The two capacitors will have some potential, say V^ . The net capacitance of the parallel combination of the two capacitors C^ =C_ 1 +C_ 2 =C+2 C+3 C The potential of the capacitors V^ = Q^ C^ = 3 CV 3 C =V The electrostatic energy of the capacitors E^ = (1)/(2) C^ V^ 2 =(1)/(2)( 3 C) V^ 2 =(3)/(2) CV^ 2

BITSAT 2015

Exam: BITSAT
Year: 2015
Subject: Physics
Chapter: Capacitance

BITSAT 2015 · Physics · Capacitance

A parallel plate capacitor of capacitance C is connected to a...

A parallel plate capacitor of capacitance

\mathrm{C}

is connected to a battery and is charged to a potential difference

\mathrm{V}

. Another capacitor of capacitance

2 \mathrm{C}

is similarly charge to a potential difference

2 \mathrm{ V}

. The charging battery is now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is A parallel plate capacitor of capacitance C is connected to a battery and is charged to a potential difference V .

A parallel plate capacitor of capacitance C is connected to a battery and is charged to a potential difference V .

Options

AZero
B $\frac{3}{2} \mathrm{CV}^{2}$
C $\frac{25}{6} \mathrm{CV}^{2}$
D $\frac{9}{2} \mathrm{CV}^{2}$

Correct answer

B. $\frac{3}{2} \mathrm{CV}^{2}$

Step-by-step solution

From the figure. The net charge shared between the capacitors Q^{\prime}=Q_{2}-Q_{2}=4 C V-C V=3 C V

<img src="/api/proxy-image?url=https%3A%2F%2Ffirebasestorage.googleapis.com%2Fv0%2Fb%2Fquantrexacademy-app.firebasestorage.app%2Fo%2Fquestions%252Ffigs%252Fpyq%252Fbitsat%252FuC14fhROzIYYJ0pa2wGnML5VYknjH1G83FGfD57wcRo.original.fullsize.png%3Falt%3Dmedia&clean=1&v=wm2" data-qx-orig-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fpyq%2Fbitsat%2FuC14fhROzIYYJ0pa2wGnML5VYknjH1G83FGfD57wcRo.original.fullsize.png?alt=media" data-qx-storage-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fpyq%2Fbitsat%2FuC14fhROzIYYJ0pa2wGnML5VYknjH1G83FGfD57wcRo.original.fullsize.png?alt=media">

\\ The two capacitors will have some potential, say

\mathrm{V}^{\prime}

. The net capacitance of the parallel combination of the two capacitors C^{\prime}=C_{1}+C_{2}=C+2 C+3 C The potential of the capacitors \mathrm{V}^{\prime}=

\frac{\mathrm{Q}^{\prime}}{\mathrm{C}^{\prime}}=\frac{3 \mathrm{CV}}{3 \mathrm{C}}=\mathrm{V}

The electrostatic energy of the capacitors \mathrm{E}^{\prime}=

\frac{1}{2} \mathrm{C}^{\prime} \mathrm{V}^{\prime 2}=\frac{1}{2}(

\mathrm{C}) \mathrm{V}^{2}=\frac{3}{2} \mathrm{CV}^{2}

Practice Capacitance on Quantrex Academy →

More from Capacitance

A parallel plate capacitor with plate area A and plate separation d=2 m has a capacitance… BITSAT 2024 A capacitor of capacitance C is charged to a potential V. The flux of the electric field… BITSAT 2023 The work done in placing a charge of 8 × 10^ -18 coulomb on a condenser of capacity 100… BITSAT 2023 In a given network the equivalent capacitance between A and B is C_ 1 =C_ 4 =1 μ F, C_ 2… BITSAT 2021 In the circuit given below, the charge in μ C, on the capacitor having 5 μ F is BITSAT 2020 When a capacitor is fully charged as shown in the following figure, then current drawn… BITSAT 2019 A charged capacitor of capacitance C is discharging through a resistor of resistance R .… BITSAT 2019 A parallel plate capacitor C with plates of unit area and separation d is filled with a… BITSAT 2018 Full Capacitance list All BITSAT PYQs