Advertisements
Advertisements
Question
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.
Advertisements
Solution
Radius of each circular plate, R = 6.0 cm = 0.06 m
Capacitance of a parallel plate capacitor, C = 100 pF = 100 × 10−12 F
Supply voltage, V = 230 V
Angular frequency, ω = 300 rad s−1
(a) The rms value of conduction current, I = `"V"/"X"_"C"`
Where,
XC = Capacitive reactance
= `1/(ω"C")`
∴ I = V × ωC
= 230 × 300 × 100 × 10−12
= 6.9 × 10−6 A
= 6.9 μA
Hence, the rms value of the conduction current is 6.9 μA.
(b) Yes, conduction current is equal to displacement current.
(c) Magnetic field is given as:
B = `(μ_0"r")/(2pi"R"^2)"I"_0`
Where,
μ0 = Free space permeability = 4π × 10−7 N A−2
I0 = Maximum value of current = `sqrt2"I"`
r = Distance between the plates from the axis = 3.0 cm = 0.03 m
∴ B = `(4pi xx 10^-7 xx 0.03 xx sqrt2 xx 6.9 xx 10^-6)/(2pi xx (0.06)^2)`
= 1.63 × 10−11 T
Hence, the magnetic field at that point is 1.63 × 10−11 T.
RELATED QUESTIONS
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
Displacement current goes through the gap between the plantes of a capacitors. When the charge of the capacitor:-
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?
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?
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 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 ______.
What is displacement current?
Which condition indicates that displacement current exists?
What magnetic effect did Maxwell propose for a time-varying electric field?
In the relay-race analogy, what picks up the baton when conduction current in the wire stops?
