MHT CET · Physics · Capacitance
A parallel plate capacitor of capacitance ' \(C\) ' is connected to a battery and charged to a potential difference ' \(V\) '. Another capacitor of capacitance 3 C is similarly charged to a potential difference 3 V . The charging battery is then disconnected and capacitors are connected in parallel to each other in such a way that positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is
- A \(\frac{3}{2} \mathrm{CV}^2\)
- B \(8 \mathrm{CV}^2\)
- C \(\frac{13}{2} \mathrm{CV}^2\)
- D \(18 \mathrm{CV}^2\)
Answer & Solution
Correct Answer
(B) \(8 \mathrm{CV}^2\)
Step-by-step Solution
Detailed explanation
As both capacitors are in parallel
\(\begin{array}{ll}
\therefore & \mathrm{C}_{\mathrm{eq}}=\mathrm{C}+3 \mathrm{C}=4 \mathrm{C} \\
& \text { Net potential, } \mathrm{V}_{\mathrm{net}}=3 \mathrm{~V}-\mathrm{V}=2 \mathrm{~V} \\
& \mathrm{~V}=\frac{1}{2} \mathrm{C}_{\mathrm{eq}} \mathrm{~V}_{\text {net }}^2=\frac{1}{2} \times 4 \mathrm{C} \times(2 \mathrm{~V})^2 \\
& \mathrm{~V}=8 \mathrm{CV}
\end{array}\)
\(\begin{array}{ll}
\therefore & \mathrm{C}_{\mathrm{eq}}=\mathrm{C}+3 \mathrm{C}=4 \mathrm{C} \\
& \text { Net potential, } \mathrm{V}_{\mathrm{net}}=3 \mathrm{~V}-\mathrm{V}=2 \mathrm{~V} \\
& \mathrm{~V}=\frac{1}{2} \mathrm{C}_{\mathrm{eq}} \mathrm{~V}_{\text {net }}^2=\frac{1}{2} \times 4 \mathrm{C} \times(2 \mathrm{~V})^2 \\
& \mathrm{~V}=8 \mathrm{CV}
\end{array}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- A disc of the moment of inertia is rotating in a horizontal plane about an axis passing through a centre and perpendicular to its plane with constant angular speed Another disc of the moment of inertia having zero angular speed is placed coaxially on a rotating disc. Now both the disc are rotating with the constant angular speed . The energy lost by the initial rotating disc isMHT CET 2017 Medium
- The height ' \(h\) ' from the surface of the earth at which the value of ' g ' will be reduced by \(64 \%\) than the value at surface of the earth is ( \(\mathrm{R}=\) radius of the earth)MHT CET 2024 Medium
- An alternating electric field of frequency is applied across the radius of a cyclotron to accelerate protons (mass ). The operating magnetic field used and K.E. of the proton beam produced by it are respectively ( charge on proton)MHT CET 2018 Hard
- A stray magnetic field does ' \(\underline{\text { NOT' }}\) affect the deflection of moving coil galvanometer becauseMHT CET 2020 Easy
- A solid sphere of mass 'M' and radius 'R' is rotating about its diameter. A disc of same mass and radius is also rotating about an axis passing through its centre and perpendicular to the plane but angular speed is twice that of the sphere. The ratio of kinetic energy of disc to that of sphere isMHT CET 2020 Medium
- A gas is compressed at constant temperature. Its molecules gainMHT CET 2011 Easy
More PYQs from MHT CET
- The difference between \(\Delta \mathrm{H}\) and \(\Delta \mathrm{U}\) is usually significant for systems consisting of:MHT CET 2023 Easy
- For a particle performing S.H.M. the displacement - time graph is shown.
For that particle the force - time graph is correctly shown in graph
MHT CET 2025 Medium - Two springs of spring constants ' \(\mathrm{K}^{\prime}\) and ' \(2 \mathrm{~K}^{\prime}\) are stretched by same force. If ' \(\mathrm{w}_{1}{ }^{\circ}\) and ' \(\mathrm{w}_{2}\) ' are the energies stored in them respectively thenMHT CET 2020 Medium
- For the cell,
\({ }^{\ominus} \mathrm{Zn}_{(s)}\left|\mathrm{Zn}^{+2}(1 \mathrm{M})\right|\left|\mathrm{Ag}^{+1}(1 \mathrm{M})\right| \mathrm{Ag}_{(s)}^{\oplus}\)
If concentration of \(\mathrm{Zn}^{+2}\) decreases to 0.1 M at 298 K . then emf of cellMHT CET 2025 Medium - If the equation given by \(h x y+10 x+6 y+4=0\) represents a pair of lines, then \(h\) is equal toMHT CET 2009 Easy
- Two cards are drawn simultaneously from a well shuffled pack of 52 cards. If \(X\) is the random variable of getting queens, then the value of \(2 E(X)+3 E\left(X^2\right)\) for the number of queens isMHT CET 2025 Medium