Q. No.In the given circuit below inductance values of \(L_1, L_2 \text { and } L_3\) are same. The magnetic energy stored in the entire circuit is \(\left(U_t\right)\) and that stored in the \(L_2\) inductor is \(\left(U_l\right) . U_t / U_l \) is:
(Ignore the mutual inductance if any)
1. \(6\)
2. \(8\)
3. \(10\)
4. \(15\)
(Ignore the mutual inductance if any)
1. \(6\)
2. \(8\)
3. \(10\)
4. \(15\)
Subtopic: Self - Inductance |
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Level 2: 60%+
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A \(30~\text{cm}\) long solenoid has \(10\) turns per cm and area of \(5~\text{cm}^2\). The current through the solenoid coil varies from \(2~\text{A}\) to \(4~\text{A}\) in \(3.14~\text{s}\). The emf induced in the coils is \(\alpha\times 10^{-5}~\text{V}\). The value \(\alpha\) is:
1. \(60\)
2. \(12\)
3. \(120\)
4. \(34\)
1. \(60\)
2. \(12\)
3. \(120\)
4. \(34\)
Subtopic: Self - Inductance |
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Inductance of a coil with \(10^4\) turns per unit length is \(10~\text{mH}\) and it is connected to a dc source of \(10~\text{V}\) with internal resistance of \(10~\Omega.\) The energy density in the inductor when the current reaches \(\left(\dfrac{1}{\mathrm{e}}\right)\) of its maximum value is \(\alpha \pi \times \frac{1}{\mathrm{e}^2}~\text{J/m}^3.\) The value of \(\alpha\) is: \(\left(\mu_0=4 \pi \times 10^{-7} ~\text{Tm/A}\right).\)
1. \(10\)
2. \(16\)
3. \(5\)
4. \(20\)
1. \(10\)
2. \(16\)
3. \(5\)
4. \(20\)
Subtopic: Self - Inductance |
Level 3: 35%-60%
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A solenoid having area \(A\) and length \(l\) is filled with a material having relative permeability \(2.\) The magnetic energy stored in the solenoid is:
1. \(\mathrm{B}^2 \mathrm{A} \ell\)
2. \(\dfrac{B^2 \mathrm{A} \ell}{2 \mu_0}\)
3. \(\dfrac{B^2 \mathrm{A} \ell}{\mu_0}\)
4. \(\dfrac{B^2 \mathrm{A} \ell}{4 \mu_0}\)
1. \(\mathrm{B}^2 \mathrm{A} \ell\)
2. \(\dfrac{B^2 \mathrm{A} \ell}{2 \mu_0}\)
3. \(\dfrac{B^2 \mathrm{A} \ell}{\mu_0}\)
4. \(\dfrac{B^2 \mathrm{A} \ell}{4 \mu_0}\)
Subtopic: Self - Inductance |
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Regarding self-inductance:
Choose the correct answer from the options given below:
| \(\mathrm{(A)}\) | The self-inductance of the coil depends on its geometry. |
| \(\mathrm{(B)}\) | Self-inductance does not depend on the permeability of the medium. |
| \(\mathrm{(C)}\) | Self-induced \(\mathrm{EMF }\) opposes any change in the current in a circuit. |
| \(\mathrm{(D)}\) | Self-inductance is electromagnetic analogue of mass in mechanics. |
| \(\mathrm{(E)}\) | Work needs to be done against self-induced \(\mathrm{EMF }\) in establishing the current. |
Choose the correct answer from the options given below:
| 1. | \(\mathrm{(A), (B), (C), (E)}\) only |
| 2. | \(\mathrm{(A), (B), (C), (D)}\) only |
| 3. | \(\mathrm{(A), (C), (D), (E)}\) only |
| 4. | \(\mathrm{(B), (C), (D), (E)}\) only |
Subtopic: Self - Inductance |
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In a coil, the current changes from \(-2\) A to \(+2\) A in \(0.2\) s and induces an emf \(0.1\) V. The self-inductance of the coil is :
1. \(4\) mH
2. \(5\) mH
3. \(2.5\) mH
4. \(1\) mH
Subtopic: Self - Inductance |
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The current through an inductor varies with time according to \(i=(3 t+2)~ \text{A},\) where \(t\) is in seconds. If the magnitude of the back EMF induced in the inductor at a certain instant is \(12~\text{V},\) what is the value of the inductance?
| 1. | \(1~\text{H}\) | 2. | \(2~\text{H}\) |
| 3. | \(4~\text{H}\) | 4. | \(5~\text{H}\) |
Subtopic: Self - Inductance |
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A \(10~\Omega\), \(20~\text{mH}\) coil carrying constant current is connected to a battery of \(20~\text{V}\) through a switch. When the switch is opened, the current becomes zero in \(100~\mu \text{s}\). The average emf induced in the coil is:
1. \(100~\text{V}\)
2. \(250~\text{V}\)
3. \(400~\text{V}\)
4. \(550~\text{V}\)
1. \(100~\text{V}\)
2. \(250~\text{V}\)
3. \(400~\text{V}\)
4. \(550~\text{V}\)
Subtopic: Self - Inductance |
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A coil of self-inductance \(2~\text{H}\) carries a current (increasing according to the law \(I=2 \sin t^2~\text{A} \)). The energy stored in the coil when the current rises from \(0~\text{A}\) to \(2~\text{A}\) is:
| 1. | \(4~\text{J}\) | 2. | \(3~\text{J}\) |
| 3. | \(1~\text{J}\) | 4. | \(6~\text{J}\) |
Subtopic: Self - Inductance |
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A coil of inductance \(1\) H and resistance \(100~\Omega\) is connected to a battery of \(6\) V. Determine approximately:
(Given: \(\mathrm{ln}2 = 0.693, e^{\frac{-3}{2}}= 0.25\))
1. \(t =10~\text{ms}; U = 2~\text{mJ}\)
2. \(t =10~\text{ms}; U = 1~\text{mJ}\)
3. \(t =7~\text{ms}; U = 1~\text{mJ}\)
4. \(t =7~\text{ms}; U = 2~\text{mJ}\)
| I. | The time elapsed before the current acquires half of its steady–state value. |
| II. | The energy stored in the magnetic field associated with the coil at an instant \(15\) ms after the circuit is switched on. |
1. \(t =10~\text{ms}; U = 2~\text{mJ}\)
2. \(t =10~\text{ms}; U = 1~\text{mJ}\)
3. \(t =7~\text{ms}; U = 1~\text{mJ}\)
4. \(t =7~\text{ms}; U = 2~\text{mJ}\)
Subtopic: Self - Inductance |
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