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In the given circuit, \( C_1 = 2 \, \mu \text{F}, \; C_2 = 0.2 \, \mu \text{F}, \; C_3 = 2 \, \mu \text{F}, \; C_4 = 4 \, \mu \text{F}, \; C_5 = 2 \, \mu \text{F}, \; C_6 = 2 \, \mu \text{F} ,\) The charge stored on capacitor \( C_4 \) is ________ \( \mu \text{C} .\)

As shown in the figure, two parallel plate capacitors having equal plate area of \( 200 \, \text{cm}^{2} \) are joined in such a way that \( a \neq b \). The equivalent capacitance of the combination is \( x \epsilon_{0} \, \text{F} \). The value of \( x \) is __________.

A \( 600 \, \text{pF} \) capacitor is charged by \( 200 \, \text{V} \) supply. It is then disconnected from the supply and is connected to another uncharged \( 600 \, \text{pF} \) capacitor. Electrostatic energy lost in the process is __________ \( \mu \text{J} \).

A capacitor has capacitance \( 5\,\mu F \) when it’s parallel plates are separated by air medium of thickness \( d \). A slab of material of dielectric constant \( 1.5 \) having area equal to that of plates but thickness \( \dfrac{d}{2} \) is inserted between the plates. Capacitance of the capacitor in the presence of slab will be (in \( \mu F \)) ____.

A parallel plate capacitor has plate area \( 40 \, \text{cm}^2 \) and plates separation \( 2 \, \text{mm} \). The space between the plates is filled with a dielectric medium of a thickness \( 1 \, \text{mm} \) and dielectric constant \( 5 \). The capacitance of the system is:

The equivalent capacitance of the combination shown is:

A parallel plate capacitor with air between the plate has a capacitance of \( 15 \, \text{pF} \). The separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant \( 3.5 \). Then the capacitance becomes \( \frac{x}{4} \, \text{pF} \). The value of \( x \) is ________ .

The distance between two plates of a capacitor is \( d \) and its capacitance is \( C_1 \), when air is the medium between the plates. If a metal sheet of thickness \( {2d}/{3} \) and of the same area of plate is introduced between the plates, the capacitance of the capacitor becomes \( C_2 \). The ratio \( {C_2}/{C_1} \) is:

In the given figure the total charge stored in the combination of capacitor is \( 100 \, \mu \text{C} \). The value of ‘x’ is __________.

A capacitor of capacitance \( C \) is charged to a potential \( V \). The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is:

A parallel plate capacitor of capacitance \( 2 \, \text{F} \) is charged to a potential \( V \), The energy stored in the capacitor is \( E_{1} \). The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is \( E_{2} \). The ratio \( {E_{2}}/{E_{1}} \) is:

Two parallel plate capacitors \( C_{1} \) and \( C_{2} \) each having capacitance of \( 10 \, \mu \text{F} \) are individually charged by a \( 100 \, \text{V} \) D.C. source. Capacitor \( C_{1} \) is kept connected to the source and a dielectric slab is inserted between it plates. Capacitor \( C_{2} \) is disconnected from the source and then a dielectric slab is inserted in it. Afterwards the capacitor \( C_{1} \) is also disconnected from the source and the two capacitors are finally connected in parallel combination. The common potential of the combination will be ______ V.

A parallel plate capacitor with plate area \( A \) and plate separation \( d \) is filled with a dielectric material of dielectric constant \( K = 4 \). The thickness of the dielectric material is \( x \), where \( x < d \).

Let \( C_{1} \) and \( C_{2} \) be the capacitance of the system for \( x = \dfrac{1}{3} d \) and \( x = \dfrac{2d}{3} \), respectively. If \( C_{1} = 2 \, \mu \text{F} \) the value of \( C_{2} \) is __________ \( \mu \text{F} \)

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JEE Main 2023 11th April Evening Shift

A capacitor of capacitance \( C \) is charged to a potential \( V \). The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is: