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Q. No.In Maxwell’s famous modification of Ampère’s law in electromagnetism, he introduced the concept of:
| 1. | AC current | 2. | DC current |
| 3. | Displacement current | 4. | Reactance |
Subtopic: Maxwell's Equations |
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A parallel-plate capacitor of capacitance \(\dfrac{1}{2}\text{ F} \) is such that an instantaneous displacement current of \(i\) ampere flows between its plates. What is the corresponding rate of change of voltage \(\dfrac{dV}{dt}\) across the capacitor?
| 1. | \(2i\) | 2. | \(\dfrac{i}{2}\) |
| 3. | \(\dfrac{1}{2i}\) | 4. | \(i\) |
Subtopic: Displacement Current |
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Displacement current exists:
| 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. |
Subtopic: Displacement Current |
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A capacitor is connected across a battery which delivers a current of \(1~\text A\) at an instant in the capacitor. Displacement current through the capacitor at that instant is:
1. \(1~\text A\)
2. \(0 ~\text A\)
3. \(2~ \text A\)
4. \(0.5~{\text{A}}\)
1. \(1~\text A\)
2. \(0 ~\text A\)
3. \(2~ \text A\)
4. \(0.5~{\text{A}}\)
Subtopic: Displacement Current |
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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. \(60~\mu\text{A}\), zero
2. zero, zero
3. zero, \(60~\mu\text{A}\)
4. \(60~\mu\text{A}, 60~\mu\text{A}\)
Subtopic: Displacement Current |
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A displacement current of \(4.425~\mu\text A\) is developed in the space between the plates of a parallel plate capacitor when voltage is changing at a rate of \(10^{6}~\text{V/s}.\) The area of each plate of the capacitor is \(40~\text{cm}^2.\) The distance between each plate of the capacitor is \(x \times 10^{-3}~\text m.\) The value of \(x\) is:
(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. \(8\)
(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. \(8\)
Subtopic: Displacement Current |
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The separation between the pate of a parallel plate capacitor is \(1\) mm is connected in an electric circuit if rate of change of voltage between the plate is \(10^8~~\text {V/s}\) and plate area is \(30 ~\text {cm}^2\), then the value of displacement current between the plate will be:
1. \( 8.85 \mathrm{~mA} \)
2. \( 3.65 \mathrm{~mA} \)
3. \(2.65 \mathrm{~mA} \)
4. \( 9.57 \mathrm{~mA} \)
1. \( 8.85 \mathrm{~mA} \)
2. \( 3.65 \mathrm{~mA} \)
3. \(2.65 \mathrm{~mA} \)
4. \( 9.57 \mathrm{~mA} \)
Subtopic: Displacement Current |
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Maxwell unified:
| 1. | electricity and gravitation |
| 2. | electricity and magnetism |
| 3. | electromagnetism with weak nuclear forces |
| 4. | none of the above |
Subtopic: Maxwell's Equations |
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Correctly match the two lists.
| List-I | List-II | ||
| (A) | Gauss's law (electrostatics) | (P) | \(\oint\vec {B}\cdot d\vec {A}=0\) |
| (B) | Ampere's circuital law | (Q) | \(\oint\vec {B}\cdot d\vec {l}=\mu_0i_{\text{enclosed}}\) |
| (C) | Gauss's law (magnetism) | (R) | \(\oint\vec E \cdot d \vec A=\dfrac{q_{_{\text{enclosed}}}}{\varepsilon_0}\) |
| (D) | Faraday's law of induction | (S) | \( \varepsilon=-\dfrac{d\phi_{_B}}{dt}\) |
| 1. | \(\mathrm{(A)\rightarrow (R)},\mathrm{(B)\rightarrow (Q)},\mathrm{(C)\rightarrow (S)}, \mathrm{(D)\rightarrow (P)}\) |
| 2. | \(\mathrm{(A)\rightarrow (R)},\mathrm{(B)\rightarrow (Q)},\mathrm{(C)\rightarrow (P)}, \mathrm{(D)\rightarrow (S)}\) |
| 3. | \(\mathrm{(A)\rightarrow (R)},\mathrm{(B)\rightarrow (S)},\mathrm{(C)\rightarrow (Q)}, \mathrm{(D)\rightarrow (P)}\) |
| 4. | \(\mathrm{(A)\rightarrow (R)},\mathrm{(B)\rightarrow (S)},\mathrm{(C)\rightarrow (P)}, \mathrm{(D)\rightarrow (Q)}\) |
Subtopic: Maxwell's Equations |
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According to the modified Ampere's circuital law (Ampere-Maxwell Law), where \(i_c\) represents the conduction current and \(i_D\) represents the displacement current, the correct equation is:
| 1. | \({\oint \vec B. d\vec{l}=\mu_0\left(i_c+\varepsilon_0\dfrac{{d}\phi_E}{dt}\right)} \) |
| 2. | \( { \oint \vec B.d\vec{l}~=~\mu_0~\varepsilon_0\dfrac{{d}\phi_E}{ dt}} \) |
| 3. | \( { \oint \vec B.d\vec{l}=\mu_0{i}} \) |
| 4. | \( { \oint \vec B. d\vec{l}=\mu_0\left(i_c\dfrac{d\phi_E}{dt}{+i_D}\right)}\) |
Subtopic: Maxwell's Equations |
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