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  • 1(current)
Q. No.
In the circuit shown in the adjoining figure, the switch was kept at the position \('1'\) for a long time. The switch \(K\) is suddenly (and smoothly) shifted to position \('2'.\)
The current through the cell, just after the shift, is:
1. \(\dfrac{V_0}{2R}\) 2. \(\dfrac{V_0}{R}\)
3. \(\dfrac{3V_0}{4R}\) 4. zero
Subtopic:  LR circuit |
Level 4: Below 35%

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The current through the inductor in the figure is initially zero. The initial rate of change of the current \(i\) through the inductor (i.e. \(\dfrac{di}{dt}\)) is:
           
 
1. zero 2. \(-\dfrac{I_{0} R}{L}\)
3. \(\dfrac{I_{0} R}{L}\) 4. \(\dfrac{I_{0} R}{2L}\)
Subtopic:  LR circuit |
Level 3: 35%-60%

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An inductor \((L)\) and a resistor \((R)\) are connected in series and a battery is connected, as shown in the figure. Once the current becomes steady, the power in the resistance is \(P_R\) and the energy stored in the inductor is \(U_L.\) The switch is suddenly (and smoothly) toggled to the position \(B\) allowing the inductor to discharge. The time in which the energy stored becomes \(\dfrac12\) its initial value is:
                           
 
1. \(\dfrac{U_L}{P_R}\) 2. \(\dfrac{U_L~\mathrm {ln}2}{P_R}\)
3. \(\dfrac{2U_L~\mathrm{ln 2}}{P_R}\) 4. \(\dfrac{2U_L}{P_R}\)
Subtopic:  LR circuit |
 55%
Level 3: 35%-60%

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The \(\text{DC}\) time constant of an \(L\)-\(R\) circuit is the same as that of an \(R\)-\(C\) circuit where the inductor in the first circuit was replaced by a capacitor. The value of the resistance \(R\) equals:
1. \(\dfrac{1}{2\pi}\sqrt{\dfrac{L}{C}}\) 2. \(\sqrt{\dfrac{L}{C}}\)
3. \(2\pi\sqrt{\dfrac{L}{C}}\) 4. \(2\sqrt{\dfrac{L}{C}}\)
Subtopic:  LR circuit |
 58%
Level 3: 35%-60%

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An inductor \((L)\) and a resistor \((R)\) are connected in series across a battery of emf \(E,\) and the circuit is switched on. The current rises steadily. The rate of increase of the current \(\left(\text{i.e.,}\dfrac {di} {dt}\right),\) when the voltage drops across the resistor is \(\dfrac{E}{2}\), is given by: \(\dfrac {di} {dt}\) = 
1. \(\dfrac{E}{L}\) 2. \(\dfrac{E}{2L}\)
3. \(\dfrac{2E}{L}\) 4. \(\dfrac{E}{L}e^{-1}\)
Subtopic:  LR circuit |
 84%
Level 1: 80%+

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