Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
This displacement current through the capacitor is given by,
`I_d = I_c = (dq)/(dt)` ......(i)
Here we are given, q = q0 cos 2πνt
Putting this value in equation (i), we get
`I_d = I_c = - q_0 sin 2pivt xx 2 piv`
`I_d = I_c = - 2 pivq_0 sin 2pivt`
APPEARS IN
संबंधित प्रश्न
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.
- Calculate the capacitance and the rate of charge of the potential difference between the plates.
- Obtain the displacement current across the plates.
- Is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor? Explain.
A parallel plate capacitor (Figure) made of circular plates each of radius R = 6.0 cm has a capacitance C = 100 pF. The capacitor is connected to a 230 V ac supply with a (angular) frequency of 300 rad s−1.
- What is the rms value of the conduction current?
- Is the conduction current equal to the displacement current?
- Determine the amplitude of B at a point 3.0 cm from the axis between the plates.
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.
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
Displacement current goes through the gap between the plantes of a capacitors. When the charge of the capacitor:-
Which of the following is the unit of displacement current?
An electromagnetic wave travelling along z-axis is given as: E = E0 cos (kz – ωt.). Choose the correct options from the following;
- The associated magnetic field is given as `B = 1/c hatk xx E = 1/ω (hatk xx E)`.
- The electromagnetic field can be written in terms of the associated magnetic field as `E = c(B xx hatk)`.
- `hatk.E = 0, hatk.B` = 0.
- `hatk xx E = 0, hatk xx B` = 0.
A variable frequency a.c source is connected to a capacitor. How will the displacement current change with decrease in frequency?
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`.
A particle is moving with speed v = b`sqrtx` along positive x-axis. Calculate the speed of the particle at time t = τ (assume that the particle is at origin at t = 0).
A parallel plate capacitor is charged to 100 × 10-6 C. Due to radiations, falling from a radiating source, the plate loses charge at the rate of 2 × 10-7 Cs-1. The magnitude of displacement current is ______.
