Home
Class 12
PHYSICS
Fig. shows a capacitor made of two circu...

Fig. shows a capacitor made of two circular plates each of radius 12 cm and separated by 5.0mm. The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to 0.15A.
(a) Calculate the capacitance and the rate of change of potential difference between the plates.
(b) Obtain the displacement current across the plates.
(c) Is Kirchhoff's first rule valid at each plate of the capacitor ? Explain.

Text Solution

Verified by Experts

Radius of each circular plate, r=12cm =0.12m
Distance between the plates, d=5cm=0.05m
Changing current, I=0.15A
permittivity of free space, `epsilon_(0)=3.85xx10^(-12)C^(2)N^(-1)m^(-2)`
(a) Capacitance between the two plates is given by the relation
`=(epsilon_(0)A)/(d)`
`C`
where A=Area of each plate `=pir^(2)`
`C=(epsilon_(0)pir^(2))/(d)`
`=(8.85xx10pi^(12)xx0.12^(2))/(0.05)`
`=8.0032xx10^(-12)F=80.032pF`
Charge on each plate, q=CV
Where,
V=potential difference across the plates
Differentiation on both sides with respect to time (t) gives :
`(dq)/(dt)=C(dV)/(dt)`
But, `(Dq)/(dt)="current"(l)`
`therefore (dv)/(dt)=(1)/(C)`
`rArr(0.15)/(80.032xx10^(-12))=1.87xx10^(9)V//s`
Therefore, the change in potential difference between the plates is `1.87xx10^(9)V//s`.
(b) The displacement current across the plates is the same as the conduction current.
Hence, the displacement current `,i_(d)` is 0.15A.
(c) Yes
Kirchhoff's first rule is valid at each plate of the capacitor provided that we take the sum of conduction and displacement for current.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • ELECTROMAGNETIC WAVES

    NCERT ENGLISH|Exercise Exercise|15 Videos
  • ELECTROMAGNETIC INDUCTION

    NCERT ENGLISH|Exercise Exercise|17 Videos
  • ELECTROSTATIC POTENTIAL AND CAPACITANCE

    NCERT ENGLISH|Exercise Exercise|37 Videos

Similar Questions

Explore conceptually related problems

Figure shows a capacitor made of two circular plates each of radius 12 cm , and separated by 5.0 cm . the capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to 0.15 A (a) Calcuate the capacitance and the rate of change of potential difference between the plates (b) Obtain the displacement current across the plates (c) Is kirchhoff's first rule(junction rule) vaild at each plate of the capacitor ? Explain. .

A capacitor, made of two parallel plates each of plate area A and separation d, is being charged by an external ac socurce. Show that the displacement current inside the same as the current charging the capacitor.

Knowledge Check

  • A capacitor made of two circular plates each of radius 12 cm and separated by 5 cm. The capacitor is being charged by an external source. The charging current is constant and equal to 0.15 A. The capacitance of the parallel plate capacitor is

    A
    40 pF
    B
    45 pF
    C
    70 pF
    D
    80 pF
  • A parallel plate air capacitor is charged to a potential difference of V volts. After disconnecting the charging battery the distance between the plates of the capacitor is increased using an isulating handle. As a result the potential difference between the plates

    A
    increases
    B
    decrease
    C
    does not charge
    D
    becomes zero
  • Similar Questions

    Explore conceptually related problems

    A capacitor, made of two parallel plates each of plate area A and separation d, is being charged by an external ac socurce. Show that the displacement current inside the same as the current charging the capacitor.

    The charging current for a capacitor is 0.25 A . What is the displacement current across its plates?

    Displacement current goes through the gap between the plates of a capacitor when the charge of the capacitor

    Displacement current goes through the gap between the plates of a capacitor when the charge of the capacitor

    In a parallel plate capacitor, the distance between the plates is d and potential difference across the plate is V . Energy stored per unit volume between the plates of capacitor is

    The force between the plates of a parallel plate capacitor of capacitance C and distance of separation of the plates d with a potential difference V between the plates, is.