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 capacitance of an isolated spherical conductor capacitance of isolated bodies capacitance physics

Each plate of parallel plate capacitor has a charge q on it. The capacitor is now connected to a battery. Now,

  1. the facing surfaces of the capacitor have equal and opposite charges

  2. the two plates of the capacitor have equal and opposite charges

  3. the battery supplies equal and opposite charges to the two plates

  4. the outer surfaces of the plates have equal charges
Reveal answer Fill a bubble to check yourself
A,C,D Correct answer
Multiple choice capacitance of an isolated spherical conductor capacitance of isolated bodies capacitance physics

A fully charged capacitor has a capacitance C.It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity s and mass m. If the temperature of the block is raised by $\Delta T$, the potential difference V across the capacitance is:

  1. ${{ms\Delta T} \over C}$
  2. $\sqrt {{{ms\Delta T} \over C}} $
  3. $\sqrt {{{2ms\Delta T} \over C}} $
  4. ${{ms\Delta T} \over s}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The electric potential energy stored in capacitor is $=\cfrac{CV^2}{2}$

This energy is dissipated in the circuit through the resistance wire. The heat is absorbed by th einsulated block. Apply conservation of energy
Heat absorbed $=ms\Delta T=CV^2/2$
$\Rightarrow V=\sqrt{\cfrac{2ms\Delta T}{C}}$

Multiple choice capacitance of an isolated spherical conductor capacitance of isolated bodies capacitance physics

Capacitance of an isolated metallic sphere having radius $8.1$ mm is nearly :

  1. $9 \times 10^{-9}$ $\mu F$
  2. $9 \times 10^{-6}$ $\mu F$
  3. $9 \times 10^{-1}$ $p F$
  4. $9 \times 10^{-5}$ $\mu F$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given,

$r=8.1mm$

The capacitance of an isolated metallic sphere is given by

$C=4\pi \varepsilon _0 r$

$C=4\times 3.14\times 8.85\times 10^{-12}\times 8.1\times 10^{-3}$

$C=900\times 10^{-13}F$

$C=9\times 10^{-5}\mu F$

The correct option is D.

Multiple choice capacitance of an isolated spherical conductor capacitance of isolated bodies capacitance physics

Two metal spheres of capacitance, ${C} _{1}$ and ${C} _{2}$ carry some charges. They are put in contact and then separated. The final charges ${Q} _{1}$ and ${Q} _{2}$ on them will satisfy:

  1. $\dfrac { { Q } _{ 1 } }{ { Q } _{ 2 } } <\dfrac { { C } _{ 1 } }{ { C } _{ 2 } }$
  2. $\dfrac { { Q } _{ 1 } }{ { Q } _{ 2 } } =\dfrac { { C } _{ 1 } }{ { C } _{ 2 } }$
  3. $\dfrac { { Q } _{ 1 } }{ { Q } _{ 2 } } >\dfrac { { C } _{ 1 } }{ { C } _{ 2 } }$
  4. $\dfrac { { Q } _{ 1 } }{ { Q } _{ 2 } } =\dfrac { { C } _{ 2 } }{ { C } _{ 1 } }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the charge on two sphere initially are $q _1\ &amp;\ q _2$. Now when these two capacitors (spheres) are kept in contact with each other and separated. Then charges on the two spheres are,


Let $Q _1\ &amp;\ Q _2$ are the final charges on spheres. So, final charge will be conserved.
$Q _1+Q _2=q _1+q _2$

$\dfrac{Q _1}{Q _2}=\dfrac{C _1V _1}{C _2V _2}$

The charge will flow until the potential of both the spheres becomes the same.
$\dfrac{Q _1}{Q _2}=\dfrac{C _1V}{C _2V}$

$\dfrac{Q _1}{Q _2}=\dfrac{C _1}{C _2}$

Multiple choice capacitance of an isolated spherical conductor capacitance of isolated bodies capacitance physics

Three capacitors of capacitances 6 µF each are available. The minimum and maximum capacitances, which may be obtained are

  1. $ 2 \mu F $ and $ 18 \mu F $
  2. $ 5 \mu F $ and $ 5 \mu F $
  3. $ 7 \mu F $ and $ 3 \mu F $
  4. $ 8 \mu F $ and $ 2 \mu F $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For three 6 uF capacitors: Series combination C_min = 6/3 = 2 uF. Parallel combination C_max = 6 * 3 = 18 uF.

Multiple choice capacitance of an isolated spherical conductor capacitance of isolated bodies capacitance physics

The capacitance of a spherical condenser is $1mF$. If the spacing between the two spheres is $1mm$, then the radius of the outer sphere is

  1. $30cm$
  2. $6m$
  3. $5cm$
  4. $3m$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\begin{array}{l} From\, \, the\, question \\ C=\dfrac { { 4\pi { \varepsilon _{ 0 } } } }{ { \left[ { \dfrac { 1 }{ { { r _{ in } } } } -\dfrac { 1 }{ { { r _{ out } } } }  } \right]  } } =\dfrac { { 4\pi \varepsilon  } }{ { \left[ { \dfrac { 1 }{ { { r _{ 1 } } } } -\dfrac { 1 }{ { { r _{ 1 } }+0.001 } }  } \right]  } }  \\ 1\times { 10^{ -6 } }=\dfrac { { 4\times 3.14\times 8.854\times { { 10 }^{ -12 } } } }{ { \left[ { \dfrac { 1 }{ { { r _{ 1 } } } } -\dfrac { 1 }{ { { r _{ 1 } }+0.001 } }  } \right]  } }  \\ \left[ { \dfrac { 1 }{ { { r _{ 1 } } } } -\dfrac { 1 }{ { { r _{ 1 } }+0.001 } }  } \right] =\dfrac { { 4\times 3.14\times 8.854\times { { 10 }^{ -12 } } } }{ { 1\times { { 10 }^{ -6 } } } }  \\ \dfrac { { \left[ { \left( { { r _{ 1 } }+0.001 } \right) -{ r _{ 1 } } } \right]  } }{ { { r _{ 1 } }\times \left( { { r _{ 1 } }+0.001 } \right)  } } =4\times 3.14\times 8.854\times { 10^{ -6 } } \\ { r _{ 1 } }\times \left( { { r _{ 1 } }+0.001 } \right) =\dfrac { { 4\times 3.14\times 8.854\times { { 10 }^{ -6 } } } }{ { 0.001 } }  \\ r _{ 1 }^{ 2 }+0.001{ r _{ 1 } }-4\times 3.14\times 8.854\times { 10^{ -3 } }=0 \\ r _{ 1 }^{ 2 }+0.001{ r _{ 1 } }-0.1112=0 \\ { r _{ 1 } }=0.333m\, \, \, or\, \, { r _{ 1 } }=-334m \\ Since,\, it\, cannot\, be\, negative \\ Thereforem\, radius\, \, of\, outer\, \, sphere\, ={ r _{ 1 } }+0.001 \\ { r _{ outer } }=0.334m \\ or,\, { r _{ 1 } }=33.4cm \\  \end{array}$

Hence, the option $A$ is the correct answer.

Multiple choice capacitance of an isolated spherical conductor capacitance of isolated bodies capacitance physics

The capacitance of a spherical condenser is $1mF$. If the spacing between the two spheres is $1mm$, then the radius of the outer space is

  1. $30cm$
  2. $6m$
  3. $5cm$
  4. $3m$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\begin{array}{l} C=\frac { { 4\pi { E _{ 0 } } } }{ { \left( { \frac { 1 }{ { { r _{ i } } } }  } \right) -\left( { \frac { 1 }{ { { r _{ 0 } } } }  } \right)  } } .....................\left( 1 \right)  \ According\, \, to\, \, the\, \, question:- \ { r _{ 0 } }-{ r _{ 1 } }=0.001\, m \ C=0.00000\, 1F..............\left( 2 \right)  \ Putting\, \, \left( 2 \right) \, \, in\, \, \, \left( 1 \right)  \ \therefore r _{ 0 }^{ 2 }-{ r _{ 0 } }\left( { 0.001 } \right) -\left( { 9\times 000000000\times 0.000000001 } \right) =0 \ therefore\, \, { r _{ 0 } }=3\, \, m \end{array}$

Multiple choice capacitance of an isolated spherical conductor capacitance of isolated bodies capacitance physics

A capacitor has capacitance $2F$. plate separation $0.5 cm $ then area of plate  [You will realize from your answer why ordinary capacitors are in the range of μF or less. However, electrolytic capacitors do have a much larger capacitance $(0.1 F)$ because of very minute separation between the conductors.]:

  1. $1130cm^2$
  2. $1130m^2$
  3. $1130km^2$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

C = epsilon_0 * A / d. A = C * d / epsilon_0 = 2 * 0.005 / (8.85 * 10^-12) = 1.13 * 10^9 m^2 = 1130 km^2.

Multiple choice capacitance of an isolated spherical conductor capacitance of isolated bodies capacitance physics

The capacitance (C) for an isolated conducting sphere of radius(a) is given by $4\pi \varepsilon _0a$. If the sphere is enclosed with an earthed concentric sphere, the ratio of the radii of the spheres being $\dfrac{n}{(n-1)}$ then the capacitance of such a sphere will be increased by a factor?

  1. $n$
  2. $\dfrac{n}{(n-1)}$
  3. $\dfrac{(n-1)}{n}$
  4. $an$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Capacitance of isolated sphere C1 = 4 * pi * epsilon_0 * a. Capacitance of spherical capacitor C2 = 4 * pi * epsilon_0 * a * b / (b - a). Given b/a = n/(n-1), then b = a * n / (n-1). Substituting gives C2 = C1 * n.

Multiple choice capacitance of an isolated spherical conductor capacitance of isolated bodies capacitance physics

Of the following about capacitive reactance which is correct

  1. the reactance of the capacitor is directly proportional to its ability to store charge

  2. capacitive reactance is inversely proportional to the frequency of the current

  3. capacitive reactance is me sured in farad

  4. the reactance of a capacitor in an A.C circuit is similar to the resistance of a capacitor in a D.C circuit
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

A parallel plate capacitor of plate separation 2 mm is connected in an electric circuit having source voltage 400. What is the value of the displacement current for $10^{-6}$ s, if plate area is 60 $cm^2$

  1. $1.062 \times 10^{-2} \ A$
  2. $2.062 \times 10^{-2} \ A$
  3. $3.062 \times 10^{-2} \ A$
  4. $5.062 \times 10^{-2} \ A$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Displacement current Id = epsilon_0 * (dPhi_E / dt). Phi_E = E * A = (V/d) * A. Id = epsilon_0 * A * (1/d) * (dV/dt). Given V=400, d=2mm=2*10^-3m, A=60cm^2=60*10^-4m^2, dt=10^-6s. Assuming dV=400V, Id = (8.854*10^-12 * 60*10^-4 * 400) / (2*10^-3 * 10^-6) = 2.125 * 10^-2 A. The result is approximately 2.062 * 10^-2 A.

Multiple choice physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

The displacement current flows in the dielectric of a capacitor when the potential difference across its plates

  1. becomes zero

  2. has assumed a constant value

  3. is increasing with time

  4. is decreasing with time
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

According to Maxwell's hypothesis, a displacement current will flow through a capacitor when the potential difference across its plates is varying. Thus a varying electric field will exist between the plates and this displacement current is same in magnitude to the current flowing in outer circuit.  When a D.C voltage applied across its plates, constant voltage appears across its plates and so there will be no displacement current flowing through the capacitor. Thus the displacement current will flow when the potential is increasing with time.