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Two identical capacitors have same capacitance \( C \). One of them is charged to the potential \( V \) and other to the potential \( 2V \). The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is:

A parallel plate capacitor of capacitance \( 12.5 \, \text{pF} \) is charged by a battery connected between its plates to potential difference of \( 12.0 \, \text{V} \). The battery is now disconnected and a dielectric slab \( (\varepsilon_r = 6) \) is inserted between the plates. The change in its potential energy after inserting the dielectric slab is ____________ \( \times 10^{-12} \, \text{J} \).

A galvanometer (\( G \)) of \( 2\,\Omega \) resistance is connected in the given circuit. The ratio of charge stored in \( C_{1} \) and \( C_{2} \) is:

A capacitor is made of a flat plate of area \( A \) and a second plate having a stair-like structure as shown in figure. If the area of each stair is \( \frac{A}{3} \) and the height is \( d \), the capacitance of the arrangement is:

In the given figure, the charge stored in \( 6 \, \mu \text{F} \) capacitor. when points \( A \) and \( B \) are joined by a connecting wire is _____ \( \mu \text{C} \).

A \( 16 \, \Omega \) wire is bend to form a square loop. A \( 9 \, \text{V} \) battery with internal resistance \( 1 \, \Omega \) is connected across one of its sides. If a \( 4 \, \mu\text{F} \) capacitor is connected across one of its diagonals, the energy stored by the capacitor will be \( \frac{x}{2} \, \mu \text{J} \), where \( x = \) __________.

The electric field between the two parallel plates of a capacitor of \( 1.5 \, \mu \text{F} \) capacitance drops to one third of its initial value in \( 6.6 \, \mu \text{s} \) when the plates are connected by a thin wire. The resistance of this wire is ________ \( \Omega \). (Given, \( \log 3 = 1.1 \))

A parallel plate capacitor with plate separation \( 5 \, \text{mm} \) is charged up by a battery. It is found that on introducing a dielectric sheet of thickness \( 2 \, \text{mm} \), while keeping the battery connections intact, the capacitor draws \( 25\% \) more charge from the battery than before. The dielectric constant of the sheet is \( \_\_\_\_\_\_\_\_ \).

The charge accumulated on the capacitor connected in the following circuit is ___________ $\mu\text{C}$. (given $C = 150\ \mu\text{F}$)

A capacitor of \( 10 \, \mu \text{F} \) capacitance whose plates are separated by \( 10 \, \text{mm} \) through air and each plate has area \( 4 \, \text{cm}^2 \) is now filled equally with two dielectric media of \( K_1 = 2, K_2 = 3 \) respectively as shown in figure. If new force between the plates is \( 8 \, \text{N} \). The supply voltage is ____ \( V \).

A capacitor has air as dielectric medium and two conducting plates of area \( 12 \,\text{cm}^{2} \) and they are \( 0.6 \,\text{cm} \) apart. When a slab of dielectric having area \( 12 \,\text{cm}^{2} \) and \( 0.6 \,\text{cm} \) thickness is inserted between the plates. One of the conducting plates has to be moved by \( 0.2 \,\text{cm} \) to keep the capacitance same as in previous case. The dielectric constant of the slab is:
(Given \( \varepsilon_{0} = 8.834 \times 10^{-12} \,\text{F/m} \))

A capacitor of capacitance \( C \) and potential \( V \) has energy \( E \). It is connected to another capacitor of capacitance \( 2C \) and potential \( 2V \). Then the loss of energy is \( \frac{x}{3} E \), where \( x \) is________.

In an electrical circuit drawn below the amount of charge stored in the capacitor is ______ \( \mu\text{C} \).

Three capacitors of capacitances \( 25 \, \mu \text{F} \), \( 30 \, \mu \text{F} \) and \( 45 \, \mu \text{F} \) are connected in parallel to a supply of \( 100 \, \text{V} \). Energy stored in the above combination is \( E \). When these capacitors are connected in series to the same supply, the stored energy is \( \frac{9}{x} E \). The value of \( x \) is __________.

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JEE Main 2024 9th April Morning Shift

A capacitor is made of a flat plate of area \( A \) and a second plate having a stair-like structure as shown in figure. If the area of each stair is \( \frac{A}{3} \) and the height is \( d \), the capacitance of the arrangement is: