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Q. No.

An electrical circuit segment contains a \(50~\text{mH}\) inductor in series with a \(30~\text{V}\) source and a \(2~\Omega\) resistor, connected between points \(P\) and \(Q\) as shown. At a certain instant, the current through the circuit is \(1~\text{A}\) and is decreasing at a rate of \(100~\text{A/s}.\) What is the potential difference \((V_P-V_Q)\) at that instant?

1. \(10\) V 2. \(25\) V
3. \(33\) V 4. \(53\) V
Subtopic:  LR circuit |
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Level 1: 80%+
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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 |
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An AC sub-circuit contains an inductor \(L\) and a resistor \(R=0.2~\Omega\) connected in series, as shown in the diagram below. At a certain instant \((V_{A}-V_{B})=0.5~\text{V}, \) \(I=0.5~\text{A}, \) and the current is increasing at the rate of \(\left(\dfrac{d i}{d t}\right)=8~\text{A/s} \). The inductance of the coil is:
                 
1. \(0.01~\text{H}\)
2. \(0.02~\text{H}\)
3. \(0.05~\text{H}\)
4. \(0.5~\text{H}\)
Subtopic:  LR circuit |
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Level 1: 80%+
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In a part of the circuit, as shown, it is given that the current is decreasing at a rate of \(1~\text{A/s}.\) Then \(V_A-V_B\) is equal to:
      
1. \(18~\text{V}\)
2. \(-18~\text{V}\)
3. \(9~\text{V}\)
4. \(-9~\text{V}\)
Subtopic:  LR circuit |
 81%
Level 1: 80%+
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\(L,\) \(C\) and \(R\) represent the physical quantities inductance, capacitance, and resistance respectively. Which of the following combinations have dimensions of frequency?
(a) \(\dfrac{1}{RC}\)

(b) \(\dfrac{R}{L}\)

(c) \(\dfrac{1}{\sqrt{{LC}}}\)

(d) \(\dfrac{C}{L}\)
Choose the correct option from the options given below:

1. (a), (b), (c)
2. (d), (c), (a)
3. (c), (d), (b)
4. (a), (d), (b)
Subtopic:  LR circuit |
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The figure below illustrates a part of a circuit. The rate of change of current in the inductor is:

1. \(-\dfrac{1}{2}~ \text{A s}^{-1}\)
2. \(-1~ \text{A s}^{-1}\)
3. \(-\dfrac{1}{4} ~\text{A s}^{-1}\)
4. \(\dfrac{1}{4} ~\text{A s}^{-1}\)
Subtopic:  LR circuit |
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Level 2: 60%+
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A coil of inductance \(2\text{ H}\) having negligible resistance is connected to a source of supply whose voltage is given by \(V = 3t \) volt. (where \(t\) is in second). If the voltage is applied when \(t = 0\), then the energy stored in the coil after \(4\text{ s}\) is:
1. \(73 \mathrm{~J}\)
2. \(36 \mathrm{~J}\)
3. \(144 \mathrm{~J}\)
4. \(288 \mathrm{~J}\)

Subtopic:  LR circuit |
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Level 2: 60%+
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