Tag: electrostatic potential and capacitance

Questions Related to electrostatic potential and capacitance

Dielectric constant for a metal is:

dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

  1. zero

  2. infinite

  3. 1

  4. 10

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Correct Option: B
Explanation:

Permittivity of metals is very high comparable to the permittivity of free space. So dielectric constant for metal is infinite.

A parallel plate condenser of capacity $10\mu F$ is connected to an A.C. supply voltage $e = 4\sin \left( {100\pi t} \right)$. The maximum displacement current:

dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

  1. $4\pi \mu A$

  2. $4\pi mA$

  3. $2.8\pi \mu A$

  4. $2\pi \mu A$

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Correct Option: B
Explanation:

Displacement current, ${i _d} = {\varepsilon _ \circ }A\frac{{dE}}{{dt}}$
where, $A$ is area and $E$ is electric field
$\begin{array}{l}E = \frac{e}{d} = \frac{{4\sin (100\pi t)}}{d}\{i _d} = {\varepsilon _ \circ }A \times \frac{1}{d}\left[ {\frac{d}{{dt}}\left( {4\sin 100\pi t} \right)} \right]\ = \frac{{{\varepsilon _ \circ }A}}{d}.4(cos100\pi t) \times 100\pi \ = C.400\pi .cos100\pi t\{\left( {{i _d}} \right) _{\max }} = \left( {10 \times {{10}^{ - 6}}} \right) \times 400\pi A\ = 4\pi  \times {10^{ - 3}}A = 4\pi mA\end{array}$

Which of the following can be used as dielectric?

dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

  1. Plastics

  2. Mica

  3. Porcelain

  4. All of the above

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Correct Option: D
Explanation:

The dielectric is a material through which no electric current passes. Here the given materials-plastic, mica and porcelain are all the  dielectric because current can not pass through them.

Which of the following is/are non-polar dielectrics?

dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

  1. $HCL$

  2. Water

  3. Benzene

  4. $NH _3$

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Correct Option: C
Explanation:

Ammonia and $HCl$ are polar molecules since they have a net dipole moment towards a particular direction. Both water and benzene are non-polar molecules. But water is a conductor of electricity, whereas benzene is a dielectric (insulator).

Breakdown voltage is
$A$. voltage at which dielectric behaves as conductor
$B$. voltage at which molecules starts flowing inside the dielectric freely.
Which of the following is correct regarding above case,

dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

  1. Both $B$, $A$ are correct

  2. $B$ is correct

  3. $A$ is correct

  4. None of the above is correct

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Correct Option: B
Explanation:

Breakdown voltage for a dielectric is the maximum voltage at which, applied electric field becomes so high that electrons break up from the molecules of dielectric and becomes free inside the dielectric due to this dielectric becomes conductive. 

Which of the following statement is false in context of dielectric?

dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

  1. Materials of polar molecules have higher dielectric constant.

  2. Materials of polar molecules have lower dielectric constant.

  3. Materials of polar molecules have higher breakdown voltage.

  4. Materials of polar molecules have lower breakdown voltage.

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Correct Option: A,D

If $C$ is the value of the capacitance of a capacitor filled with a given dielectric and $a$ is the capacitance of an identical capacitor in a vacuum, the dielectric constant, symbolized by the Greek letter kappa, , is simply expressed as

dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

  1. $\dfrac{C}{a}$

  2. $\dfrac{a}{C}$

  3. $C\times a$

  4. None 

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Correct Option: A
Explanation:

The capacitance of a parallel plate capacitor filled with the given material of dielectric constant $\kappa$ is given by:

              $C=\dfrac{\kappa\varepsilon _{0}A}{d}$ .....................eq1
And the capacitance of the same capacitor without the given material is given by:
              $a=\dfrac{\varepsilon _{0}A}{d}$  .....................eq2
Dividing eq1 by eq2:
              $C/a=\kappa$

The value of the dielectric constant at room temperature (25 C, or 77 F) for air is 

dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

  1. $1.00059 $

  2. $2.00059 $

  3. $0.0009 $

  4. $0.00059 $

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Correct Option: A
Explanation:

The value of dielectric constant for air at room temperature $ (25^{o}C , or 77^{o}F )$ is $1.00059$ .

Which of the following is polar dielectrics?

dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

  1. $HCL$

  2. $NH _3$

  3. $H _2O$

  4. All of the above

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Correct Option: D
Explanation:

Polar dielectric are those in which center of positive and negative charge is not same due to their shapes. 

$HCl$ , $NH _{3}$ and $H _{2}O$ all are polar dielectrics due to their high dielectric constant formed due to the difference in the polarity.

The insertion of a dielectric between the plates of a parallel-plate capacitor always 

dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

  1. increases its capacitance 

  2. decreases its capacitance 

  3. remains same its capacitance 

  4. none of the above 

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Correct Option: A
Explanation:

The capacitance of a parallel plate capacitor completely filled with a given material of dielectric constant $K$ is given by:

              $C=\dfrac{K\varepsilon _{0}A}{d}$ .....................eq1
And the capacitance of the same capacitor without the given material is given by:
              $C'=\dfrac{\varepsilon _{0}A}{d}$  .....................eq2
Dividing eq1 by eq2:
              $C/C'=K$
As $K>1$ always, hence $C>C'$ i.e. the insertion of a dielectric between the plates of a parallel -plate capacitor always increases the capacitance.