Q. No.In the figure magnetic energy stored in the coil is:
| 1. | Zero | 2. | Infinite |
| 3. | \(25\) joules | 4. | None of the above |
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1. \(\dfrac{E^{2}}{2 R}\)
2. \(\dfrac{E^{2} L}{2 R^{2}}\)
3. \(\dfrac{E^{2} L}{R}\)
4. \(\dfrac{E^{2} L}{2 R}\)
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When the current in the portion of the circuit shown in the figure is \(2\) A and increases at the rate of \(1\) A/s, the measured potential difference \(V_{ab}=8\) V. However, when the current is \(2\) A and decreases at the rate of \(1\) A/s, the measured potential difference \(V_{ab}= 4\) V. The value of \(R\) and \(L\) is:
| 1. | \(3~\Omega\) and \(2~\text{H}\) respectively |
| 2. | \(3~\Omega\) and \(3~\text{H}\) respectively |
| 3. | \(2~\Omega\) and \(1~\text{H}\) respectively |
| 4. | \(3~\Omega\) and \(1~\text{H}\) respectively |
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The figure shows three circuits with identical batteries, inductors, and resistors. Rank the circuits according to the current, in descending order, through the battery \((i)\) just after the switch is closed and \((ii)\) a long time later:
| 1. | \((i)~ i_2>i_3>i_1\left(i_1=0\right) (ii) ~i_2>i_3>i_1\) |
| 2. | \((i)~ i_2<i_3<i_1\left(i_1 \neq 0\right) (ii)~ i_2>i_3>i_1\) |
| 3. | \((i) ~i_2=i_3=i_1\left(i_1=0\right) (ii)~ i_2<i_3<i_1\) |
| 4. | \((i)~ i_2=i_3>i_1\left(i_1 \neq 0\right) (ii) ~i_2>i_3>i_1\) |
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The key \(K\) is inserted at time \(t=0\). The initial \((t=0)\) and final \(t\rightarrow \infty\) currents through the battery are:
1. \(\frac{1}{15}~\text{A},~\frac{1}{10}~\text{A}\)
2. \(\frac{1}{10}~\text{A},~\frac{1}{15}~\text{A}\)
3. \(\frac{2}{15}~\text{A},~\frac{1}{10}~\text{A}\)
4. \(\frac{1}{15}~\text{A},~\frac{2}{25}~\text{A}\)
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The network shown in figure is a part of a complete circuit. If at a certain instant, the current \(i\) is \(10\) A and is increasing at the rate of \(4\times 10^{3}\) A/sec, then \(V_A-V_B\) is:
| 1. | \(6\) V | 2. | \(-6\) V |
| 3. | \(10\) V | 4. | \(-10\) V |
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In the circuit diagram shown in figure, \(R = 10~\Omega\), \(L = 5~\text{H},\) \(E = 20~\text{V}\) and \(i = 2~\text{A}\). This current is decreasing at a rate of \(1.0\) A/s. \(V_{ab}\) at this instant will be:
| 1. | \(40\) V | 2. | \(35\) V |
| 3. | \(30\) V | 4. | \(45\) V |
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The resistance in the following circuit is increased at a particular instant. At this instant the value of resistance is \(10~\Omega.\) The current in the circuit will be:
| 1. | \(i = 0.5~\text{A}\) | 2. | \(i > 0.5~\text{A}\) |
| 3. | \(i < 0.5~\text{A}\) | 4. | \(i = 0\) |
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A series combination of inductance \((L)\) and resistance \((R)\) is connected to a battery of emf \(E\). The final value of current depends on:
| 1. | \(L\) and \(R\) | 2. | \(E\) and \(R\) |
| 3. | \(E\) and \(L\) | 4. | \(E\), \(L\), and \(R\) |
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Switch \(S\) of the circuit shown in the figure is closed at \(t=0\). If \(e\) denotes the induced emf in \(L\) and \(i\) denotes the current flowing through the circuit at time \(t\), then which of the following graphs is correct?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
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