(B) The initial capacitance of the air capacitor is $C_0 = \frac{\epsilon_0 A}{d} = 1 \mu F$.From the figure,the two dielectrics are placed in paralle

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(B) The initial capacitance of the air capacitor is $C_0 = \frac{\epsilon_0 A}{d} = 1 \mu F$.From the figure,the two dielectrics are placed in parallel,each occupying half the area of the plates $(A_1 = A_2 = A/2)$ and the full distance $d$ between the plates.The capacitance of the two parts are:$C_1 = \frac{K_1 \epsilon_0 (A/2)}{d} = K_1 \frac{C_0}{2} = 8 \times \frac{1}{2} = 4 \mu F$$C_2 = \frac{K_2 \epsilon_0 (A/2)}{d} = K_2 \frac{C_0}{2} = 4 \times \frac{1}{2} = 2 \mu F$Since they are in parallel,the equivalent capacitance is $C_{eq} = C_1 + C_2 = 4 \mu F + 2 \mu F = 6 \mu F$.

Class 12 Physics Electric Potential and Capacitance Effect of Dielectric Inside Capacitor

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An air capacitor has a capacitance of $1 \mu F$. Now,the space between the two plates of the capacitor is filled with two dielectrics as shown in the figure. The capacitance of the capacitor is ($d=$ distance between two plates,$K_1=8$ and $K_2=4$ are the dielectric constants of the two dielectrics respectively).

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A
$12 \mu F$
B
$6 \mu F$
C
$\frac{8}{3} \mu F$
D
$3 \mu F$

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Class 12

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Electric Potential and Capacitance

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Effect of Dielectric Inside Capacitor

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DifficultJEE MAIN 2021

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Medium

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The capacitance of a spherical capacitor in air is $50 \,\mu F$. When it is immersed in oil,its capacitance becomes $110 \,\mu F$. Calculate the dielectric constant of the oil.

Easy

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DifficultAP EAMCET 2004

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$A$ parallel plate capacitor with air medium between the plates has a capacitance of $10 \mu F$. The area of the capacitor is divided into two equal halves and filled with two media (as shown in the figure) having dielectric constants $K_1=2$ and $K_2=4$. The capacitance of the system will be (in $\mu F$)

MediumMHT CET 2023

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$A$ parallel plate capacitor has a capacity $C$. The separation between the plates is doubled and a dielectric medium is introduced between the plates. If the capacity now becomes $2C$,the dielectric constant of the medium is

The capacitance of a spherical capacitor in air is $50 \,\mu F$. When it is immersed in oil,its capacitance becomes $110 \,\mu F$. Calculate the dielectric constant of the oil.

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