Two identical capacitors, have the same capacitance $C$. One of them is charged to potential $V_1$ and the other to $V_2$. The negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the combined system is
Two identical capacitors, have the same capacitance $C$. One of them is charged to potential $V_1$ and the other to $V_2$. The negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the combined system is
- A
$\frac{1}{4}C\left( {V_1^2 - V_2^2} \right)$
- B
$\frac{1}{4}C\left( {V_1^2 + V_2^2} \right)$
- C
$\frac{1}{4}C{\left( {{V_1} - {V_2}} \right)^2}$
- D
$\frac{1}{4}C{\left( {{V_1} + {V_2}} \right)^2}$
Similar Questions
The plates of a parallel plate capacitor have an area of $90 \,cm ^{2}$ each and are separated by $2.5\; mm .$ The capacitor is charged by connecting it to a $400\; V$ supply.
$(a)$ How much electrostatic energy is stored by the capacitor?
$(b)$ View this energy as stored in the electrostatic field between the plates, and obtain the energy per unit volume $u$. Hence arrive at a relation between $u$ and the magnitude of electric field $E$ between the plates.
The plates of a parallel plate capacitor have an area of $90 \,cm ^{2}$ each and are separated by $2.5\; mm .$ The capacitor is charged by connecting it to a $400\; V$ supply.
$(a)$ How much electrostatic energy is stored by the capacitor?
$(b)$ View this energy as stored in the electrostatic field between the plates, and obtain the energy per unit volume $u$. Hence arrive at a relation between $u$ and the magnitude of electric field $E$ between the plates.
A capacitor of capacitance $C$ is charged to potential difference $V_0$. Now this capacitor is connected to an ideal inductor. When $25\%$ of energy of capacitor is transferred to inductor then at that time what will be potential difference across capacitor
A capacitor of capacitance $C$ is charged to potential difference $V_0$. Now this capacitor is connected to an ideal inductor. When $25\%$ of energy of capacitor is transferred to inductor then at that time what will be potential difference across capacitor
A $16\ \Omega$ wire is bend to form a square loop. A $9 \mathrm{~V}$ battery with internal resistance $1\ \Omega$ is connected across one of its sides. If a $4\ \mu \mathrm{F}$ capacitor is connected across one of its diagonals, the energy stored by the capacitor will be $\frac{x}{2} \ \mu \mathrm{J}$. where $x=$________.
A $16\ \Omega$ wire is bend to form a square loop. A $9 \mathrm{~V}$ battery with internal resistance $1\ \Omega$ is connected across one of its sides. If a $4\ \mu \mathrm{F}$ capacitor is connected across one of its diagonals, the energy stored by the capacitor will be $\frac{x}{2} \ \mu \mathrm{J}$. where $x=$________.
- [JEE MAIN 2024]
A parallel plate capacitor is charged to a potential difference of $50\, V$. It is discharged through a resistance. After $1$ second, the potential difference between plates becomes $40 \,V$. Then
A parallel plate capacitor is charged to a potential difference of $50\, V$. It is discharged through a resistance. After $1$ second, the potential difference between plates becomes $40 \,V$. Then
A parallel plate capacitor of capacitance $C$ is connected to a battery and is charged to a potential difference $V$. Another capacitor of capacitance $2C$ is connected to another battery and is charged to potential difference $2V$. The charging batteries are 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 $V$. Another capacitor of capacitance $2C$ is connected to another battery and is charged to potential difference $2V$. The charging batteries are 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
- [IIT 1995]