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.
Advertisements
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
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?
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 parallel plate capacitor of plate separation 2 mm is connected in an electric circuit having source voltage 400 V. What is the value of the displacement current for 10-6 second if the plate area is 60 cm2?
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 ______
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?
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?
AC voltage V(t) = 20 sinωt of frequency 50 Hz is applied to a parallel plate capacitor. The separation between the plates is 2 mm and the area is 1 m2. The amplitude of the oscillating displacement current for the applied AC voltage is ______.
[take ε0 = 8.85 × 10-12 F/m]
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 ______.
A parallel plate capacitor made of circular plates is being charged such that the surface charge density on its palates is increasing at a constant rate with time. The magnetic field arising due to displacement current is ______.
A parallel plate capacitor is charged by connecting it to a battery through a resistor. If I is the current in the circuit, then in the gap between the plates, there is no conduction current:
In the Ampere–Maxwell Circuital Law, what produces a changing magnetic field in addition to current?
How do displacement current and conduction current compare in the charging capacitor?
How does displacement current apply when charging a smartphone?
What role does displacement current have in radio wave transmission?
