Physics

Capacitors and Capacitance

186 Questions

Capacitors and capacitance are crucial topics in physics, covering the storage of electric charge and energy. These concepts explore series and parallel combinations, dielectric materials, and capacitive reactance. Questions frequently appear in various competitive engineering and medical entrance exams.

Series and parallel capacitorsParallel plate capacitorsCapacitive reactance formulasDielectrics and permittivitySpherical capacitors

Capacitors and Capacitance Questions

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

When a metal plate is introduced between the two plates of a charged capacitor and insulated from them, then

  1. the metal plate divides the capacitor into two capacitors connected in parallel to each other

  2. the metal plate divides the capacitor into two capacitors connected in series with each other

  3. the metal plate is equivalent to a dielectric of zero dielectric constant

  4. the metal plate is equivalent to a dielectric of infinite dielectric constant
Reveal answer Fill a bubble to check yourself
B,D Correct answer
Explanation

The capacitor is divided into two capacitors joined in series. So (b) is correct. Also as K for a metal is $\infty$, therefore (d) is also correct.

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

Dielectric constant, property of an electrical insulating material (a dielectric) equal to

  1. the ratio of the capacitance of a capacitor filled with the given material to the capacitance of an identical capacitor in a vacuum without the dielectric material.

  2. the ratio of the capacitance of a capacitor filled with the given material to the capacitance of an identical capacitor in a vacuum with the dielectric material.

  3. the capacitance of a capacitor filled with the given material

  4. none of the above

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The capacitance of a parallel plate capacitor filled with the 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,
              $C/C'=K$

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

 The capacitance of a capacitor

  1. filled with a dielectric is lesser than it would be in a vacuum.

  2. filled with a dielectric is greater than it would be in a vacuum.

  3. filled with a dielectric is same as it would be in a vacuum.

  4. none of the above

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The capacitance of a parallel plate capacitor filled with dielectric of dielectric constant $K$ is,

           $C=\dfrac{K\varepsilon _{o}A}{d}$  ..................eq1
and the capacitance of a parallel plate capacitor without dielectric in a vacuum is,
           $C'=\dfrac{\varepsilon _{o}A}{d}$  ...................eq2
Dividing eq1 by eq2 , we get
            $C=KC'$
as $K>1$ , therefore $C>C'$ therefore the capacitance of a capacitor filled with a dielectric is greater than it would be in a vacuum.

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

The voltage can be increased, but electric breakdown will occur if the electric field inside the capacitor becomes too large. The capacity can be increased by 

  1. expanding the electrode areas

  2. reducing the gap between the electrodes

  3. expanding the gap between the electrodes

  4. Both A and B
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The capacitance of an air filled parallel plate capacitor is given by:

            $C=\dfrac{\varepsilon _{0}A}{d}$  ..........................eq1
where $A=$ area of each plate (electrode),
            $d=$ distance between plates (electrodes)
from eq1 ,
           $C\propto A$
It is clear that capacity C can be increased by expanding the electrodes area,
and     $C\propto 1/d$ ,
hence, capacity C can be increased by reducing the gap between the electrodes.

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

A dielectric slab of thickness $6 cm$ is placed between the plates of a parallel plate capacitor. If the distance between plates is reduced by $4 cm$, the capacity of the capacitor remains the same. Find the dielectric constant of the medium.

  1. $2$
  2. $4$
  3. $6$
  4. $3$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
 for a parallel plate capacitor 
             C = ε K   A / d
It is possible that we have air/vacuum and then a medium in between the parallel plates.  Initially there is a medium of dielectric constant K and of thickness d.

    Let  K1 be the dielectric constant of the slab.  
     let d1 be the thickness of slab = 6cm.

Formula for capacity with multiple media in between the plates is 
             C =  ε A / [ d1/K1 + d2 / K ]
          total gap =  d1 + d2 = d + 4 cm          =>  d2 = d + 4 cm - 6 cm = d - 2
 
         d / K =  d1/ K1 + d2 / K 
         d/ K = 6 / K1  + (d-2)/K

          d - (d-2)  = 6 K / K1 
                K1 = 3 K
  If there was air originally in between the plates,  K = 1,  then answer is 3.
Multiple choice dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

A parallel plate condenser is charged to $100$ volt. In this context which one of the following statements is true?

  1. The two plates attract each other

  2. There is to force between the plates

  3. The two plates of the condenser repel each other

  4. The force between the plates can be attractive or repulsive depending upon the nature of the dielectric material between the plates
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Oppositely charged plates of a capacitor attract each other due to the electrostatic force between the plates. Each plate experiences an attractive force toward the other plate.

Multiple choice physics electric fields introduction to electrostatic force electric force charging and discharging

To construct an air filled capacitor which can store $ 12 \mu C $ of charge, What can be the minimum plate area of the capacitor? (Dielectric strength of air is $3\times 10^6 V/m$ )

  1. $0.25 m^2$
  2. $0.45 m^2$
  3. $4.5 m^2$
  4. $0.35 m^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The maximum electric field (dielectric strength) for an air-filled parallel plate capacitor is E = V / d = (Q / C) / d = Q / (epsilon_0 * A). Rearranging for area gives A = Q / (epsilon_0 * E). Substituting the values: A = 12 * 10^-6 / (8.85 * 10^-12 * 3 * 10^6) = 12 * 10^-6 / (26.55 * 10^-6) = 12 / 26.55 is approximately 0.45 m^2.

Multiple choice physics electric fields introduction to electrostatic force electric force charging and discharging

A capacitor is a perfect insulator for:

  1. constant direct current

  2. alternating current

  3. direct as well as alternating current

  4. variable direct current.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A capacitor consists of two conductors separated by an insulator. In a DC circuit, it blocks current once charged. In an AC circuit, it allows current to flow due to the changing electric field, but it is still physically an insulator between the plates.

Multiple choice physics energy transformations and energy transfers forms of energy and energy conservation energy for everything forms of energy

A charged parallel plate capacitor of distance ($d$) has ${U} _{0}$ energy. A slab of dielectric constant ($K$) and thickness ($d$) is then introduced between the plates of the capacitor. The new energy of the system is given by:

  1. $K{U} _{0}$
  2. ${K}^{2}{U} _{0}$
  3. $\cfrac{{U} _{0}}{K}$
  4. $\cfrac{{U} _{0}}{{K}^{2}}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When a dielectric slab of constant K completely fills the space between the plates of a charged disconnected capacitor, the capacitance increases by a factor of K, becoming C equals K times C0. Since the charge remains constant, the stored energy U equals Q squared divided by 2C, which means the new energy becomes the initial energy divided by K.

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

The capacitance of two capacitors are $C _1=(5 \pm 0.1)\mu F$ and $C _2=(10 \pm 0.1)\mu F$, If they are connected in series then the percentage error is 

  1. $3.33 $%
  2. $4.03 $%
  3. $3.0 $%
  4. $4.33 $%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When two capacitors are in series, the equivalent capacitance is $C=\dfrac{C _1C _2}{C _1+C _2}$
Thus, $\dfrac{\Delta C}{C}=\dfrac{\Delta C _1}{C _1}+\dfrac{\Delta C _2}{C _2}+\dfrac{\Delta C _1+\Delta C _2}{C _1+C _2}$

The % error, $\dfrac{\Delta C}{C}\times 100=\left(\dfrac{\Delta C _1}{C _1}+\dfrac{\Delta C _2}{C _2}+\dfrac{\Delta C _1+\Delta C _2}{C _1+C _2}\right)\times 100$
                                         $=(\dfrac{0.1}{5}+ \dfrac{0.1}{10}+\dfrac{0.1+0.1}{5+10})\times 100=4.33$%

Multiple choice physics static electricity properties of charges charge properties of charge

A parallel late condenser consists of two circular plate each of radius $8cm$ separated by a distance of $2mm$. It is charged by an external source, with a constant charging current of $0.15$ A. The displacement.curcent is

  1. $0.10A$
  2. $0.15A$
  3. $0.20A$
  4. $0.30A$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Displacement current inside a capacitor is equal to the conduction current charging the capacitor plates. Since the charging current is given as 0.15 A, the displacement current is also 0.15 A.

Multiple choice physics static electricity properties of charges charge properties of charge

Two metallic spheres, one hollow and the other solid, have same diameter. The hollow sphere will hold charge

  1. Same as the solid sphere

  2. 2 times as the solid sphere
  3. $\displaystyle\frac{1}{2}$ times as the solid sphere

  4. Zero
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The capacity of the metallic sphere is proportional to the radius. It does not matter whether it is solid or hollow. Therefore the hollow sphere will hold same charge as the solid sphere.

Multiple choice

The capacitance of a capacitor is:

  1. The ability of a capacitor to store charge

  2. The amount of charge stored on a capacitor

  3. The ratio of charge to voltage on a capacitor

  4. All of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The capacitance of a capacitor is the ratio of charge to voltage on a capacitor.

Multiple choice

The capacitive reactance of a capacitor is:

  1. Directly proportional to frequency

  2. Inversely proportional to frequency

  3. Independent of frequency

  4. Dependent on the capacitance value
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Capacitive reactance decreases with increasing frequency, as the capacitor opposes the change in voltage more strongly at higher frequencies.

Multiple choice

What is the relationship between permittivity and capacitance?

  1. Permittivity is directly proportional to capacitance

  2. Permittivity is inversely proportional to capacitance

  3. Permittivity is independent of capacitance

  4. Permittivity is inversely proportional to the square of capacitance
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Permittivity and capacitance are directly proportional, meaning that as permittivity increases, capacitance also increases.