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Q. No.As shown in the figure, in a steady state, the charge stored in the capacitor is \(x \times 10^{-6}\) C. The value of \(x \) is:
1. 20
2. 10
3. 30
4. 40
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A wire of resistance \(R_1\) is drawn out so that its length is increased by twice its original length. The ratio of new resistance to original resistance is:
1. \(9:1\)
2. \(1:9\)
3. \(4:1\)
4. \(3:1\)
1. \(9:1\)
2. \(1:9\)
3. \(4:1\)
4. \(3:1\)
Subtopic: Derivation of Ohm's Law |
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Two coils require \(20\) minutes and \(60\) minutes respectively to produce the same amount of heat energy when connected separately to the same source. If they are connected in parallel arrangement to the same source; the time required to produce the same amount of heat by the combination of coils will be:
1. \(10\) min
2. \(30\) min
3. \(15\) min
4. \(25\) min
1. \(10\) min
2. \(30\) min
3. \(15\) min
4. \(25\) min
Subtopic: Heating Effects of Current |
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The variation of applied potential, \(V\) and the current, \(I\) flowing through a given wire is shown in the figure. The length of the wire is \(31.4~\text{cm}.\) The diameter of the wire is measured as \(2.4\) cm. The resistivity of the given wire is measured as \(x\times 10^{-3}~\Omega \text-\text{cm}.\) The value of \(x\) is:
(take \(\pi= 3.14\))
1. \(146\)
2. \(142\)
3. \(140\)
4. \(144\)
(take \(\pi= 3.14\))
1. \(146\)
2. \(142\)
3. \(140\)
4. \(144\)
Subtopic: Derivation of Ohm's Law |
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For the network shown below, the value \(V_B-V_A\) is:
1. \(10\) V
2. \(15\) V
3. \(20\) V
4. \(25\) V
1. \(10\) V
2. \(15\) V
3. \(20\) V
4. \(25\) V
Subtopic: Kirchoff's Voltage Law |
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A capacitor is discharging through a resistor \(R.\) Consider in time \(t_1,\) the energy stored in the capacitor reduces to half of its initial value and in time \(t_2,\) the charge stored reduces to one-eighth of its initial value. The ratio \(\frac{t_1}{t_2}=\)
1. \(1/2\)
2. \(1/3\)
3. \(1/4\)
4. \(1/6\)
1. \(1/2\)
2. \(1/3\)
3. \(1/4\)
4. \(1/6\)
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The combination of two identical cells, whether connected in series or parallel combination provides the same current through an external resistance of \(2~\Omega\). The value of the internal resistance of each cell is:
1. \(2~\Omega\)
2. \(4~\Omega\)
3. \(6~\Omega\)
4. \(8~\Omega\)
1. \(2~\Omega\)
2. \(4~\Omega\)
3. \(6~\Omega\)
4. \(8~\Omega\)
Subtopic: Grouping of Cells |
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Two resistors are connected in series across a battery as shown in the figure. If a voltmeter of resistance \(2000~\Omega\) is used to measure the potential difference across \(500~\Omega\) resistor, the reading of the voltmeter will be:
1. \(8\) V
2. \(4\) V
3. \(2\) V
4. \(1\) V
1. \(8\) V
2. \(4\) V
3. \(2\) V
4. \(1\) V
Subtopic: Combination of Resistors |
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Two metallic wires of identical dimensions are connected in series. If \(\sigma _1\) and \(\sigma_2\) are the conductivities of these wires respectively, the effective conductivity of the combination is:
| 1. | \(\dfrac{\sigma_1 \sigma_2}{\sigma_1+\sigma_2} \) | 2. | \(\dfrac{2 \sigma_1 \sigma_2}{\sigma_1+\sigma_2} \) |
| 3. | \(\dfrac{\sigma_1+\sigma_2}{2 \sigma_1 \sigma_2} \) | 4. | \(\dfrac{\sigma_1+\sigma_2}{\sigma_1 \sigma_2}\) |
Subtopic: Combination of Resistors |
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The current \(I\) flowing through the given circuit will be:
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)
Subtopic: Combination of Resistors |
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