Q. No.
A parallel plate capacitor is made of circular plates each of radius \(R=6.0~\text{cm}\) has a capacitance \(C=100~\text{pF}.\) The capacitor is connected to a \(230~\text V\) AC supply with an (angular) frequency of \(300~\text{rad/s}.\) The amplitude of \(\vec{B}\) at the point \(3~\text{cm}\) from the axis between the plate is:
1. \(1.12\times 10^{-11}~\text T\)
2. \(2.01\times 10^{-12}~\text T\)
3. \(1.63\times 10^{-11}~\text T\)
4. \(1.01\times 10^{-12}~\text T\)
Displacement current goes through the gap between the plates of a capacitor when the charge of the capacitor:
| (a) | increases |
| (b) | decreases |
| (c) | does not change |
| (d) | is zero |
Choose the correct option:
1. (a), (b)
2. (b), (c)
3. only (c)
4. (a), (d)
(the permittivity of free space, \(\epsilon_0=8.85\times10^{-12}~\text{C}^2 \text{N}^{-1} \text{m}^{-2}\) )
1. \(2\)
2. \(4\)
3. \(6\)
4. \(8\)
Displacement current through a capacitor at a steady state is:
| 1. | infinite | 2. | zero |
| 3. | \(\dfrac{\varepsilon_0d\phi_E}{dt}\) | 4. | \(\dfrac{\varepsilon_0d\phi_B}{dt}\) |
\(V=V_0 \sin \omega t\)
The displacement current between the plates of the capacitor would then be given by:
| 1. | \( I_d=\dfrac{V_0}{\omega C} \sin \omega t \) | 2. | \( I_d=V_0 \omega C \sin \omega t \) |
| 3. | \( I_d=V_0 \omega C \cos \omega t \) | 4. | \( I_d=\dfrac{V_0}{\omega C} \cos \omega t\) |
1. \( 800~ \text{V} / \text{s} \)
2. \( 500~ \text{V} / \text{s} \)
3. \( 200~ \text{V} / \text{s} \)
4. \( 400 ~\text{V} / \text{s}\)
A parallel plate capacitor of capacitance \(20~\mu\text{F}\) is being charged by a voltage source whose potential is changing at the rate of \(3~\text{V/s}.\) The conduction current through the connecting wires, and the displacement current through the plates of the capacitor would be, respectively:
| 1. | zero, zero | 2. | zero, \(60~\mu\text{A}\) |
| 3. | \(60~\mu\text{A},\) \(60~\mu\text{A}\) | 4. | \(60~\mu\text{A},\) zero |
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:
| 1. | A displacement current of magnitude equal to \(i\) flows in the same direction as \(i.\) |
| 2. | A displacement current of magnitude equal to \(i\) flows in the opposite direction to \(i.\) |
| 3. | A displacement current of magnitude greater than \(i\) flows but it can be in any direction. |
| 4. | There is no current. |
| 1. | when an electric field is changing in the circuit. |
| 2. | when an electric field is constant. |
| 3. | when an electric field is absent. |
| 4. | always exists independent of the electric field. |
A capacitor is made of two circular plates each of radius \(12~\text{cm}\) and separated by \(5.0~\text{cm}.\) The capacitor being charged by an external source. The charging current is constant and equal to \(0.15~\text{A}.\) The displacement current across the plates is:
1. \(0\)
2. \(0.14~\text{A}\)
3. \(0.16~\text{A}\)
4. \(0.15~\text{A}\)
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