36Capacitance

📚
CAPACITANCE
▢ Electric Capacitance:
❖ Definition: Capacitors are charge-storing devices
❖ Capacitance: Ratio of charge given to conductor/capacitor to potential to which it is raised
❖ Formula: \(C=\frac{Q}{V}\)

Table 1: Capacitance Basics

Quantity
Value / Unit
SI unit
Farad
CGS unit
Statfarad
Conversion
\(1\ Farad=9\times10^{11}\ statfarad\)
Dimensional formula
\([M^{-1}L^{-2}T^4A^2]\)
▢ Capacitance of Spherical Conductor:
❖ Formula: \(C=4\pi\epsilon_0R=\frac{R}{9\times10^9}\)

Table 1: Spherical Conductor

Quantity
Formula / Value
Radius
\(R\)
Capacitance
\(C=4\pi\epsilon_0R\)
Capacitance of earth
\(7.12\times10^{-4}\ F\)
Capacitance of earth
\(712\ \mu F\)
▢ Parallel Plate Capacitor:
❖ Definition: Two conductors separated by an insulator/dielectric; conductors carry equal and opposite charges \(\pm Q\)

Table 1: Parallel Plate Capacitor Formulae

Condition
Capacitance
Air/vacuum as dielectric
\(C=\frac{\epsilon_0A}{d}\)
Dielectric constant \(K\) fills entire space
\(C=\frac{K\epsilon_0A}{d}\)
Dielectric slab of thickness \(t
\(C=\frac{\epsilon_0A}{d-t+\frac{t}{K}}\)
Conducting slab of thickness \(t
\(C=\frac{\epsilon_0A}{d-t}\)
Conducting slab fills entire space \((t=d)\)
\(C\to\infty\)
❖ Symbols:
  • •
    \(A\) = area of each plate
  • •
    \(d\) = separation between plates
  • •
    \(K\) or \(\epsilon_r\) = dielectric constant
❖ Depends On:
  • •
    Size of plates
  • •
    Shape of plates
  • •
    Relative position/separation of plates
  • •
    Nature of medium between plates
❖ Does Not Depend On:
  • •
    Material of plates
  • •
    Potential difference between plates
  • •
    Charge given to plates
❖ Use: Produces uniform electric field between plates; outside plates, electric field is approximately zero
❖ Good Dielectric Material: High dielectric constant + high dielectric strength
▢ Insertion of Dielectrics:
❖ Dielectrics in Series:
◉ **table:
    ❖ Dielectrics in Parallel:
    ◉ **table:
      ❖ To Keep Capacitance Constant After Inserting Slab:
      ◉ Formula: \(x=t\left(1-\frac{1}{K}\right)\)
      ◉ Meaning: Plate separation must be increased by \(x\)
      ▢ Combination of Capacitors:

      Table 1: Series vs Parallel Combination

      Feature
      Series
      Parallel
      Connection
      Negative plate of one connected to positive plate of next
      Positive plates connected together and negative plates connected together
      Charge
      Same on each capacitor
      \(q=q_1+q_2+q_3+...\)
      Potential difference
      \(V=V_1+V_2+V_3+...\)
      Same across each capacitor
      Equivalent capacitance
      \(\frac{1}{C_s}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}+...\)
      \(C_p=C_1+C_2+C_3+...\)
      Effect on capacity
      Decreases
      Increases
      \(n\) identical capacitors each \(C\)
      \(C_s=\frac{C}{n}\)
      \(C_p=nC\)
      Voltage/charge distribution
      \(V_1:V_2:V_3=\frac{1}{C_1}:\frac{1}{C_2}:\frac{1}{C_3}\)
      \(Q_1:Q_2:Q_3=C_1:C_2:C_3\)
      ❖ Important Relations:
      • •
        \(\frac{C_p}{C_s}=n^2\)
      • •
        \(n=\sqrt{\frac{C_p}{C_s}}\)
      ▢ Spherical Capacitor:

      Table 1: Concentric Spherical Capacitor

      Condition
      Capacitance
      Outer sphere earthed
      \(C=\frac{4\pi\epsilon_0Kr_ar_b}{r_b-r_a}\)
      Inner sphere earthed
      \(C=\frac{4\pi\epsilon_0Kr_b^2}{r_b-r_a}\)
      ❖ Symbols:
      • •
        \(r_a\) = radius of inner sphere
      • •
        \(r_b\) = radius of outer sphere
      ▢ Energy Stored in Charged Capacitor:
      ❖ Statement: Capacitor stores charge as well as electric potential energy

      Table 1: Energy Stored

      Quantity
      Formula
      Energy stored
      \(U=\frac{Q^2}{2C}\)
      Energy stored
      \(U=\frac{1}{2}QV\)
      Energy stored
      \(U=\frac{1}{2}CV^2\)
      Energy supplied by battery
      \(\frac{Q^2}{C}=CV^2\)
      Energy density
      \(u=\frac{1}{2}\epsilon_0E^2\)
      Energy density in dielectric
      \(u=\frac{1}{2}\epsilon_0KE^2\)
      ❖ Important Point: Energy is stored in electric field between the plates
      ▢ Force Between Plates of Capacitor:

      Table 1: Force Formulae

      Form
      Formula
      Using charge
      \(F=\frac{q^2}{2\epsilon_0A}\)
      Using capacitance and voltage
      \(F=\frac{CV^2}{2d}\)
      Using surface charge density
      \(F=\frac{\sigma^2A}{2\epsilon_0}\)
      Using electric field
      \(F=\frac{1}{2}\epsilon_0E^2A\)
      ▢ Regrouping of Capacitors:
      ❖ Statement: When charged capacitors are connected by wire, charge flows from higher potential to lower potential until common potential is attained
      ❖ Like Plates Connected:

      Table 1: Two Capacitors Connected Like-to-Like

      Quantity
      Formula
      Charge conservation
      \(C_1V_1+C_2V_2=(C_1+C_2)V\)
      Common potential
      \(V=\frac{C_1V_1+C_2V_2}{C_1+C_2}\)
      Initial energy
      \(U_i=\frac{1}{2}C_1V_1^2+\frac{1}{2}C_2V_2^2\)
      Final energy
      \(U_f=\frac{1}{2}(C_1+C_2)V^2\)
      Loss in energy
      \(\Delta U=\frac{1}{2}\frac{C_1C_2}{C_1+C_2}(V_1-V_2)^2\)
      Final charge on \(C_1\)
      \(q'_1=C_1V\)
      Final charge on \(C_2\)
      \(q'_2=C_2V\)
      ❖ Unlike Plates Connected:

      Table 1: Two Capacitors Connected Unlike-to-Unlike

      Quantity
      Formula
      Common potential
      \(V=\frac{C_1V_1-C_2V_2}{C_1+C_2}\)
      Loss in energy
      \(\Delta U=\frac{C_1C_2(V_1+V_2)^2}{2(C_1+C_2)}\)
      ❖ Final Energy Ratio: \(\frac{U_1}{U_2}=\frac{C_1}{C_2}\)
      ❖ Two Identical Capacitors:
      • •
        \(V=\frac{V_1+V_2}{2}\)
      • •
        Final charge is half of net charge
      ❖ Two Spheres Joined:

      Table 1: Two Spheres of Radii \(R_1,R_2\)

      Quantity
      Formula
      Common potential
      \(V=\frac{R_1V_1+R_2V_2}{R_1+R_2}\)
      Loss in energy
      \(\Delta U=\frac{4\pi\epsilon_0R_1R_2(V_1-V_2)^2}{2(R_1+R_2)}\)
      ▢ Battery Connected vs Disconnected:
      ❖ Rule:
      • •
        Battery disconnected → charge remains constant
      • •
        Battery connected → potential difference remains constant

      Table 1: Effect of Inserting Dielectric

      Quantity
      Battery connected
      Battery disconnected
      \(Q=CV\)
      Increases
      Constant
      \(C=KC_0\)
      Increases
      Increases
      \(V=Q/C\)
      Constant
      Decreases
      \(E\)
      No change
      Decreases
      \(U\)
      Increases
      Decreases
      \(F\)
      Increases
      Decreases
      \(\sigma=Q/A\)
      Increases
      No change

      Table 2: Effect of Moving Plates Apart

      Quantity
      Battery connected
      Battery disconnected
      \(Q=CV\)
      Decreases
      Constant
      \(C=\frac{\epsilon_0A}{d}\)
      Decreases
      Decreases
      \(V=Q/C\)
      Constant
      Increases
      \(E\)
      Decreases
      No change
      \(U\)
      Decreases
      Increases
      \(F\)
      Decreases
      No change
      \(\sigma=Q/A\)
      Decreases
      No change
      ▢ Charging of Capacitor:
      ❖ Statement: Potential and charge do not reach final value instantaneously

      Table 1: Charging Through Resistance \(R\)

      Quantity
      Formula
      Charge
      \(q=q_0(1-e^{-t/RC})\)
      Potential
      \(V=V_0(1-e^{-t/RC})\)
      Current
      \(I=I_0e^{-t/RC}\)
      Initial current
      \(I_0=\frac{V_0}{R}\)
      Time constant
      \(\tau=RC\)
      ❖ Time Constant Meaning:
      • •
        Time in which charge grows to 63.2% of final value
      • •
        Time in which current falls to 36.8% of initial value
      ▢ Discharging of Capacitor:
      ❖ Statement: When charged capacitor discharges through resistance \(R\), charge, voltage and current fall exponentially

      Table 1: Discharging Through Resistance \(R\)

      Quantity
      Formula
      Charge
      \(q=q_0e^{-t/RC}\)
      Potential
      \(V=V_0e^{-t/RC}\)
      Current
      \(I=I_0e^{-t/RC}\)
      Time constant
      \(\tau=RC\)
      ❖ Rate of Discharging: Depends on time constant \(RC\)
      ▢ Multiple Drops Combined:
      ❖ Condition: \(n\) drops each of radius \(r\), charge \(q\), capacitance \(C\), potential \(V\), energy \(U\), field \(E\), surface charge density \(\sigma\) combine to form one bigger drop
      ❖ _*table:
        ▢ Metal Foil and Multiplate Capacitors:
        ❖ **table:
          ▢ Special Capacitor Networks:

          Table 1: Network Results

          Network / Condition
          Result
          Triangular/ladder type network given in source
          \(C'=\frac{n(n+1)C}{2}\)
          Infinite repeated network type
          \(C'=2C\)
          Balanced bridge condition
          \(\frac{C_1}{C_2}=\frac{C_3}{C_4}\)
          Balanced bridge result
          \(C_5\) is ineffective; no charge stored in \(C_5\)
          ▢ Read and Digest:

          Table 1: Important Capacitance Points

          Fact
          Answer
          Capacitor in AC circuit
          Works
          Capacitor in DC circuit
          Acts as perfect insulator after charging
          Energy in charged capacitor
          Stored in electric field between plates
          Net charge on capacitor
          Zero
          Practical dielectric in parallel plate capacitor
          Mica
          Reason for mica
          High dielectric strength and high dielectric constant
          Electric field between capacitor plates
          Independent of distance between plates
          Electric field with dielectric
          \(E=\frac{\sigma}{\epsilon_0K}\)
          Energy stored in capacitor
          \(\frac{Q^2}{2C}\) or \(\frac{1}{2}CV^2\)
          Energy supplied by battery
          \(\frac{Q^2}{C}\) or \(CV^2\)
          To increase potential difference
          Connect capacitors in series
          Dielectric in isolated parallel plate air capacitor
          Force between plates does not change if field is constant
          Removing one plate effect on force on charged particle
          Force becomes \(\frac{F}{2}\)
          Surface area of spherical conductor increased by \(K\) times
          Capacitance becomes \(\sqrt K\) times
          Capacitance of earth
          \(712\ \mu F\)
          Charged capacitor with one plate submerged in liquid
          Liquid level rises
          Dielectric strength of air at STP
          \(3\times10^6\ V/m\)
          Capacitors joined together
          Charge flows from higher potential to lower potential
          Thin metal foil between plates
          Capacitance remains constant
          ▢ High-Yield Recall:

          Table 1: Capacitance One-Liners

          Fact
          Answer
          Capacitor
          Charge-storing device
          Capacitance
          \(C=\frac{Q}{V}\)
          Unit
          Farad
          CGS unit
          Statfarad
          1 Farad
          \(9\times10^{11}\ statfarad\)
          Spherical conductor capacitance
          \(C=4\pi\epsilon_0R\)
          Earth capacitance
          \(712\ \mu F\)
          Parallel plate capacitor
          \(C=\frac{\epsilon_0A}{d}\)
          With full dielectric
          \(C=\frac{K\epsilon_0A}{d}\)
          Partial dielectric slab
          \(C=\frac{\epsilon_0A}{d-t+\frac{t}{K}}\)
          Conducting slab
          \(C=\frac{\epsilon_0A}{d-t}\)
          Series capacitors
          \(\frac{1}{C_s}=\frac{1}{C_1}+\frac{1}{C_2}+...\)
          Parallel capacitors
          \(C_p=C_1+C_2+...\)
          n identical series capacitors
          \(C_s=\frac{C}{n}\)
          n identical parallel capacitors
          \(C_p=nC\)
          Ratio \(C_p/C_s\)
          \(n^2\)
          Energy stored
          \(U=\frac{Q^2}{2C}=\frac{1}{2}QV=\frac{1}{2}CV^2\)
          Energy supplied by battery
          \(CV^2\)
          Energy density
          \(u=\frac{1}{2}\epsilon_0E^2\)
          Force between plates
          \(F=\frac{q^2}{2\epsilon_0A}\)
          Battery disconnected
          Charge constant
          Battery connected
          Potential constant
          Charging charge equation
          \(q=q_0(1-e^{-t/RC})\)
          Charging current equation
          \(I=I_0e^{-t/RC}\)
          Discharging charge equation
          \(q=q_0e^{-t/RC}\)
          Time constant
          \(RC\)
          Charge after one time constant during charging
          63.2% of final value
          Current after one time constant
          36.8% of initial value
          Like plates connected common potential
          \(V=\frac{C_1V_1+C_2V_2}{C_1+C_2}\)
          Unlike plates connected common potential
          \(V=\frac{C_1V_1-C_2V_2}{C_1+C_2}\)
          Energy loss after sharing
          \(\Delta U=\frac{1}{2}\frac{C_1C_2}{C_1+C_2}(V_1-V_2)^2\)
          Dielectric strength of air
          \(3\times10^6\ V/m\)
          n drops combined radius
          \(R=n^{1/3}r\)
          n drops combined potential
          \(V'=n^{2/3}V\)
          n drops combined energy
          \(U'=n^{5/3}U\)
          Balanced capacitor bridge
          \(\frac{C_1}{C_2}=\frac{C_3}{C_4}\)
          Q1.
          In a charged capacitor the energy resides
          📅IOM 2011
          Q2.
          A parallel plate capacitor is charged and the charging battery is then disconnected. If the plates of the capacitor are moved further apart by means of insulating handles:
          📅TOM 2010
          Q3.
          A 4 μF condenser is charged to 400V and then its plates are joined through a resistance of 1kΩ. The heat produced in the resistance is
          📅MOE 2012
          Q4.
          A glass slab of uniform thickness is introduced between the plates of a parallel plate capacitor. The capacity of capacitor
          📅MOE 2012
          Q5.
          A 600 μF capacitor is charged at the steady rate of 50 μc/sec. How long will it take to raise its potential to 10 volt?
          📅MOE 2068
          Q6.
          Two capacitors 1 μF & 2 μF are charged to 300v & 150v respectively and connected by a wire. The potential of the connected system is
          📅MOE 2010
          Q7.
          Two capacitors of of charges Q1 & Q2 with different capacitances are charged to the same potential V. They are then connected by a wire. The resulting potential will be
          📅MOE 2009
          Q8.
          The capacitance of a capacitor is independent of
          📅KU 2010
          Q9.
          The energy stored in a capacitor of capacitance 'C' and potential 'V' is given by
          📅KU 2009
          Q10.
          If an electron enters into a space between the plates of a parallel plate capacitor at an angle α with the plates and leaves at an angle β to the plates. The ratio of its K.E. while entering the capacitor to that while leaving will be?
          📅BP 2009
          Q11.
          Capacity of an isolated sphere is increased n times when it is enclosed by an earthed concentric sphere. The ratio of their radii is
          📅BP 2009
          Q12.
          In a parallel plate capacitor, force on each plate is
          📅I.E 2009
          Q13.
          The capacitance of a sphere of radius 1 m is
          📅I.E 2009
          Q14.
          An Aluminium foil of negligible thickness is placed between two plates of a parallel plate capacitor. Then its capacitance
          📅I.E 2009
          Q15.
          The equivalent capacitance of given circuit across A and B is
          📅MOE 2014)
          Q16.
          The capacity of a parallel plate capacitor is C. It's capacity when the separation between the plates is halved will be
          📅MOE 204
          Q17.
          Two capacitors of charges Q1 and Q2 with different capacitances are charged to the same potential V. They are then connected by a wire. The resulting potential will be
          📅MOE 09
          Q18.
          Four capacitors of capacitance 3 μF, 3 μF, 3 μF and 2 μF are arranged in the form of a rectangle then the equivalent capacitance across 2 μF capacitor is
          📅Bangladesh 09
          Q19.
          8 small drop of capacitance and radius 'r' combines to form a big drop of radius R then the capacitance of big drop will be
          📅IOM 2066
          Q20.
          The dielectric constant εr is given by the relation
          📅Bangladesh Emb.
          Q21.
          In an air parallel plate capacitor, the separation between the plates is doubled, if this cause doubling of the capacitance of the capacitor then the dielectric constant is
          📅MOE 2055
          Q22.
          In a parallel-plate capacitor of area 2 m2 a dielectric of relative permittivity 6 is inserted. Then the capacitance becomes ....... of the original value
          📅MOE 20541
          Q23.
          23 Two parallel plate capacitor of capacitance C separated by a distance have the energy stored E. Now one of the plates is moved so that distance between them is doubled (without disconnecting from battery). What will be the new energy stored?
          📅MOE 2061
          Q24.
          In a parallel plate capacitor, force on each plate is
          Q25.
          25.) What is the capacitance between point A and B?
          📅BPKIHS-95
          Q26.
          If the earth is supposed to be metallic sphere of radius 6400 km. What is its capacitance?
          📅BPKIHS-04
          Q27.
          In A. C. motor capacitor is used
          📅BPKIHS 2000
          Q28.
          When a slab is introduced in parallel plate capacitor then
          📅ΙE-02
          Q29.
          A condenser having a capacity 50 microfarad is charged to 10 volts. Its energy is:
          📅IOM 08)
          Q30.
          Two capacitors of 2 μf are charged to potential of 10 volt and 6 volt respectively. They are then joined together with like polarity. Their common potential will be
          📅MOE 066
          Q31.
          A parallel plate air capacitor has a capacitance 18 μF. If the distance between the plate is trebled and a dielectric medium is introduced, the capacitance becomes 72 μF. The dielectric constant of the medium is
          Q32.
          A 80O μF capacitor is charged at a steady rate of 50 μF/sec. How long will it take to raise its potential to 10Volt?
          Q33.
          Two condensers of capacity 0.3 μF and 0.6 μF respectively are connected in series. The combination is connected across a potential of 6 volt. The ratio of energies stored by condensers will be
          Q34.
          A 4 μF condenser is charged to 400V and then its plates are joined through a resistance of 1 kΩ. The heat produced in the resistance is:
          Q35.
          The plates of a parallel plate capacitor are charged up to 100 volt. A 2mm thick slab is inserted between the plates, then to maintain the same p.d., the distance between the capacitor plates is increased by 1.6mm. The dielectric constant of the slab is:
          Q36.
          Force acting upon a charged particle kept between the plates of a charged condenser is F. If one of the plates of the condenser is removed then the force acting on the same particle will become
          Q37.
          A parallel plate capacitor has a capacitance of 50pf in air and 105pf, when immersed in oil. The dielectric constant of the oil is:
          Q38.
          Two capacitors of capacitance 2 μF and 6 μF are connected in series. A p.d. of 800V is applied to the outer plates of the two capacitor system. The charge on each capacitor will be
          Q39.
          A parallel plate capacitor is filled with two dielectrics as shown in figure. Its capacity has ratio with capacity without dielectric as
          Q40.
          The capacity of a parallel plate condenser is 5 μF. When a glass plate is placed between the plates of the condenser, its p.d reduces to 1/8 of the original value. The magnitude of relative dielectric constant of glass is
          📅IOM•BPKIHS
          Q41.
          A parallel plate capacitor with air as medium between the plates has a capacitor of 10 μF. Now area of the capacitor is divided into the two equal halves and then filled with two media having dielectric constants K_1 = 2 and K_2 = 4. The capacitance of the system will now be
          Q42.
          A capacitor connected to a 10V battery collects a charge of 40 μC with air a dielectric and 100 μC with a given oil as dielectric. The dielectric constant of the oil is
          Q43.
          A parallel plate capacitor having dielectric slab of ϵ_r = 6 is connected across a battery and charged. This dielectric slab is then removed and new dielectric slab of ϵ_r = 10 is introduced. The ratio of energy stored in first to that in second case is
          Q44.
          With air as dielectric a capacitor connected to a 10V d.c. source collects a charge of 40 μC. When a certain oil is introduced as dielectric, the same capacitor collects a charge of 200 μC from same d.c. source. The dielectric constant of oil is :
          Q45.
          A parallel plate capacitor is charged and then isolated. When the effect of increasing the plate separation on charge, potential, capacitance, respectively?
          Q46.
          A parallel plate condenser is immersed in an oil of dielectric constant 2. The field between the plate is
          Q47.
          A parallel plate air capacitor has a capacitance of 100 μF. The plates are at a distance d apart. A slab of thickness t (t
          Q48.
          There are 10 condensers each of capacity 5 μF. The ratio between max. and min. capacity obtained from these condenser will be
          Q49.
          Two capacitors of 3 μF and 6 μF are connected in series across a potential difference of 120V. Then the p.d. Across 3 μF capacitor is
          Q50.
          A metal foil of negligible thickness is introduced between two plates of a capacitor at the centre. The capacitance of capacitor will be
          📅I.E. 2009
          Q51.
          Two insulated charged spheres of radii 20cm and 25cm respectively and having an identical charge Q connected by a copper wire and then separated.
          Q52.
          Two capacitors of 2 μF and 4 μF are connected in parallel. A third capacitor of 6 μF is connected in series. The combination is connected across a 12 V battery. The voltage across 2 μF capacitor is
          Q53.
          A capacitor is connected to a cell of emf E and some internal resistance. The p.d. across the
          Q54.
          Capacitance of a capacitor becomes 4/3 times its original value if a dielectric slab of thickness t = d/2 is inserted between the plates (d = separation between the plates). The dielectric constant of the slab is
          Q55.
          A capacitor is filled with an insulator and a certain potential difference is applied to its plates. The energy stored in the capacitor is U. Now, the capacitor is disconnected from the source and the insulator is pulled out of the capacitor. The work performed against the forces of electric field in pulling out the insulator is 4U. Then dielctric constant of the insulator is
          Q56.
          A 10 μF capacitor and a 20 μF capacitor are connected in series across 200V supply line. The charged capacitors are then disconnected from the line and reconnected with the positive plate together and negative plates together and no external voltage is applied. What is the potential difference across each capacitor?
          Q57.
          A 10 μF capacitor is charged to a potential difference of 50V and is connected to another uncharged capacitor in parallel. Now the common potential becomes 20 volt. The capacitance of second capacitor is
          Q58.
          68. A capacitor is charged to store an energy U. The charging battery is disconnected. An identical capacitor is now connected to the first capacitor in parallel. The energy in each of the capacitor is
          Q59.
          A parallel plate capacitor is filled by copper plate of thickness b. The new capacity will be
          Q60.
          A capacitor of capacity C1 is charged by connecting it across a battery of e.m.f. Vo. The battery is then removed and the capacitor is connected in parallel with an unchanged capacitor of capacity C2. The potential difference across this combination is
          Q61.
          Two capacitors C and 2C are connected in parallel and charged with V volt each. Battery is disconnected and . then a lielectric of constant K is inserted in C. Find the final p.d. of each capacitor .
          📅BPKIHS
          Q62.
          Two insulated spheres of 3 μF and 5μF are charged to 300V and 500V respectively The energy loss when they are connected by a wire is
          Q63.
          If a dielectric of K = 5 is put between the plates of a charged capacitor, the charge on capacitor will become (initial charge vas Q)
          Q64.
          A 1μF capacitor and a 2 μF capacitor are connected in parallel across a 1200 volts line The capacitors e then disconnected from the line and from each other. These . two capacitors are now connected to each other in parallel with terminals of unlike signs together. The charges on the capacitors will now be
          Q65.
          A condenser of capacity C1 is charged to a potential V_0. The electrostatic potential energy stored in it is U_o. It is connected to another uncharged condenser of capacity C2 in parallel. The energy dissipated in the process is
          Q66.
          A spherical condenser has inner and outer spheres of radii a and b respectively. The space between the two is filled with air. The difference between the capacities of two condensers formed when outer sphere is earthed and when inner sphere is earthed will be
          Q67.
          The equivalent capacitance of the combination shown when C = 45 μF is
          📅KU 2015
          Q68.
          A parallel plate capacitor has capacitance of 50 μF in air and 110 μF when immersed in oil. The dielectric constant of oil is
          📅IOM 2015