Advertisements
Advertisements
प्रश्न
A parallel-plate capacitor of plate-area A and plate separation d is joined to a battery of emf ε and internal resistance R at t = 0. Consider a plane surface of area A/2, parallel to the plates and situated symmetrically between them. Find the displacement current through this surface as a function of time.
उत्तर
Electric field strength for a parallel plate capacitor,
`E = Q/(∈_0A)`
Electric flux linked with the area,
`phi_E = EA = Q/(∈_0A) xx A/2 = Q/(2∈_0)`
Displacement current ,
`I_d = ∈_0 (dphi_E)/dt = ∈_0 d/dt(Q/(∈_0 2))`
`I_d = 1/2((dQ)/dt)` ....(i)
Charge on the capacitor as a function of time during charging,
`Q = εC[1 - e^(-t"/"RC)]`:
Putting this in equation (i), we get :
`I_d = 1/2 εC d/dt(1 - e^(-t"/"RC))`
`I_d = 1/2 εC(-e^(-t"/"RC)) xx (-1/(RC))`
`C = (A∈_0)/d`
⇒ `I_d = ε/(2R) xx e^(-(td)/(ε_0AR))`
APPEARS IN
संबंधित प्रश्न
The charging current for a capacitor is 0.25 A. What is the displacement current across its plates?
A capacitor has been charged by a dc source. What are the magnitude of conduction and displacement current, when it is fully charged?
When an ideal capacitor is charged by a dc battery, no current flows. However, when an ac source is used, the current flows continuously. How does one explain this, based on the concept of displacement current?
Without the concept of displacement current it is not possible to correctly apply Ampere’s law on a path parallel to the plates of parallel plate capacitor having capacitance C in ______.
Displacement current is given by ______.
If the total energy of a particle executing SHM is E, then the potential energy V and the kinetic energy K of the particle in terms of E when its displacement is half of its amplitude will be ______.
A spring balance has a scale that reads 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this spring, when displaced and released, oscillates with a period of 0.60 s. What is the weight of the body?
A cylinder of radius R, length Land density p floats upright in a fluid of density p0. The cylinder is given a gentle downward push as a result of which there is a vertical displacement of size x; it is then released; the time period of resulting (undampe (D) oscillations is ______.
The displacement of a particle from its mean position is given by x = 4 sin (10πt + 1.5π) cos (10πt + 1.5π). The motion of the particle is
Which of the following is the unit of displacement current?
According to Maxwell's hypothesis, a changing electric field gives rise to ______.
A capacitor of capacitance ‘C’, is connected across an ac source of voltage V, given by V = V0 sinωt The displacement current between the plates of the capacitor would then be given by ______.
A capacitor of capacitance ‘C’, is connected across an ac source of voltage V, given by
V = V0sinωt
The displacement current between the plates of the capacitor would then be given by:
The charge on a parallel plate capacitor varies as q = q0 cos 2πνt. The plates are very large and close together (area = A, separation = d). Neglecting the edge effects, find the displacement current through the capacitor?
Show that average value of radiant flux density ‘S’ over a single period ‘T’ is given by S = `1/(2cmu_0) E_0^2`.
You are given a 2 µF parallel plate capacitor. How would you establish an instantaneous displacement current of 1 mA in the space between its plates?
Sea water at frequency ν = 4 × 108 Hz has permittivity ε ≈ 80 εo, permeability µ ≈ µo and resistivity ρ = 0.25 Ω–m. Imagine a parallel plate capacitor immersed in seawater and driven by an alternating voltage source V(t) = Vo sin (2πνt). What fraction of the conduction current density is the displacement current density?
A long straight cable of length `l` is placed symmetrically along z-axis and has radius a(<< l). The cable consists of a thin wire and a co-axial conducting tube. An alternating current I(t) = I0 sin (2πνt) flows down the central thin wire and returns along the co-axial conducting tube. The induced electric field at a distance s from the wire inside the cable is E(s,t) = µ0I0ν cos (2πνt) In `(s/a)hatk`.
- Calculate the displacement current density inside the cable.
- Integrate the displacement current density across the cross-section of the cable to find the total displacement current Id.
- Compare the conduction current I0 with the displacement current `I_0^d`.
Draw a neat labelled diagram of displacement current in the space between the plates of the capacitor.
