Capacitors Quiz 1

Question 1

There are two isolated spherical capacitors with radius $${{R}_{1}}$$ and $${{R}_{2}}$$ respectively.If $${{R}_{1}}<{{R}_{2}}$$. Then capacitance: $$ \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/4d9d5d46-21a8-49e0-94d9-7fdaf6112e4f3951933395765111259.png"/>

Accepted Answer

$${{C}_{2}} > {{C}_{1}}$$

Answer

$${{C}_{1}} > {{C}_{2}}$$

Answer

$${{C}_{1}} = {{C}_{2}}$$

Answer

$$Zero$$

Question 2

A capacitor of $$C=3\mu F$$ is charged with a battery of $$5$$ volt. The plate separation is $$d$$.When it achieves maximum charge, the battery is disconnected and the plates of the capacitor are pulled apart to distance $$''2d''$$. Now the charge and potential on each capacitor: $$ \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/b626eb45-3fed-4418-8c16-71523d476a527314382083673487583.png"/>

Accepted Answer

charge remains constant, potential gets doubled

Answer

charge gets halved, potential remains constant

Answer

charge remains constant, potential remains constant too

Answer

charge gets doubled, potential remains constant

Question 3

Two identical capacitors of capacitance $$''C''$$ are connected in series to a battery of emf $$''E''$$. The first capacitor is filled completely with a dielectric of dielectric constant $$3$$, while in the second capacitor a metal slab of thickness $$\dfrac{1}{3}$$ times the separation of plates the capacitor is inserted between the plates. The amount of charge stored after the insertion of dielectric and metal slab is $$ \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/ee511d2c-2aa1-4fc6-ac2f-45191c8c08597945301347559321492.png"/>

Accepted Answer

twice that of charge stored initially

Answer

thrice that of charge stored initially

Answer

half of charge stored initially

Answer

four times of that of charge stored initially

Question 4

In a parallel plate capacitor of area $$''A''$$ and separation $$''d''$$, two dielectric slabs of width $$\dfrac{d}{3}$$ each and dielectric constants $${{k}_{1}}$$ and $${{k}_{2}}$$ respectively, are inserted. The first dielectric is inserted in contact with the first plate, and the second dielectric is placed in contact with the other plate. Calculate the new capacitance of the capacitor. $$ \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/9170ddd2-5894-459b-a24a-eb6842b2ba727740534562568820666.png"/>

Accepted Answer

$$\dfrac{3{{\varepsilon }_{0}}A}{d}\left( \dfrac{{{k}_{1}}{{k}_{2}}}{{{k}_{2}}+{{k}_{1}}{{k}_{2}}+{{k}_{2}}} \right)$$

Answer

$$\dfrac{3{{\varepsilon }_{0}}A}{d}\left( {{k}_{1}}+{{k}_{2}}+1 \right)$$

Answer

$$\dfrac{3{{\varepsilon }_{0}}A}{d}\left( \dfrac{{{k}_{1}}	imes {{k}_{2}}}{{{k}_{1}}+{{k}_{2}}+1} ight)$$

Answer

$$\dfrac{3{{\varepsilon }_{0}}A}{d}\left( 1+\dfrac{{{k}_{1}}{{k}_{2}}}{{{k}_{1}}+{{k}_{2}}} \right)$$

Question 5

If in a given circuit, find the ratio of equivalent capacitance when switch is open and closed respectively.$${{C}_{1}}=2\mu F$$, $${{C}_{2}}=4\mu F$$, $${{C}_{3}}=3\mu F$$, $${{C}_{4}}=5\mu F$$ $$ \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/b82495fc-7898-49ac-931a-e18dd09ea0fa3235484761334537316.png"/>

Accepted Answer

$$\dfrac{77	imes 7}{45	imes 12}$$

Answer

$$1:1$$

Answer

$$\dfrac{12	imes 45}{77	imes 7}$$

Answer

$$\dfrac{25}{12}$$