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Q. No.The figure given below shows an \(LCR\) series circuit with two switches \(S_1\) and \(S_2.\) When switch \(S_1\) is closed keeping \(S_2\) open, the phase difference \((\phi)\) between the current and source voltage is \(30^\circ\) and phase difference is \(60^\circ\) when \(S_2\) is closed keeping \(S_1\) open. The value of \((3L_1 - L_2)\) is: (in H)
1. \(\dfrac{9}{2} \)
2. \( \dfrac{2}{9} \)
3. \(\dfrac{1}{3}\)
4. \(3\)
1. \(\dfrac{9}{2} \)
2. \( \dfrac{2}{9} \)
3. \(\dfrac{1}{3}\)
4. \(3\)
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An inductor of inductance \(10~\text{mH}\) having resistance of \(100~\Omega\)
1. \(4/3\)
2. \(3/4\)
3. \(5/3\)
4. \(3/5\)
1. \(4/3\)
2. \(3/4\)
3. \(5/3\)
4. \(3/5\)
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A LCR series circuit driven with \(E_{r m s}=90 ~\text{V}\) at frequency \(f_d=30~\text{Hz}\) has resistance \(R=80~\Omega,\) an inductance with inductive reactance \(X_L=20.0~\Omega\) and capacitance with capacitive reactance \(X_C=80.0~\Omega.\) The power factor of the circuit is:
1. \(0.8\)
2. \(0.64\)
3. \(0.9\)
4. \(0.5\)
1. \(0.8\)
2. \(0.64\)
3. \(0.9\)
4. \(0.5\)
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An a.c. source of angular frequency \(\omega\) is connected across a resistor \(R\) and a capacitor \(C\) in series. The current is observed as \(I.\) Now the frequency of the source is changed to \(\dfrac{\omega}{4}\), (keeping the voltage unchanged) the current is found to be \(\dfrac{I}{3}\). The ratio of resistance to reactance at frequency \(\omega\) is:
1. \(\sqrt{\dfrac{6}{7}}~\)
2. \(\sqrt{\dfrac{3}{5}}\)
3. \(\sqrt{\dfrac{7}{8}}\)
4. \(\sqrt{\dfrac{3}{4}}\)
1. \(\sqrt{\dfrac{6}{7}}~\)
2. \(\sqrt{\dfrac{3}{5}}\)
3. \(\sqrt{\dfrac{7}{8}}\)
4. \(\sqrt{\dfrac{3}{4}}\)
Subtopic: Β Different Types of AC Circuits |
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A series \(LCR\) circuit with \(R=20~ \Omega, L=1.6 ~\text{H}\) \({C}=40~ \mu \text{F}\)
1. \(200\)
2. \(450\)
3. \(100\)
4. \(150\)
1. \(200\)
2. \(450\)
3. \(100\)
4. \(150\)
Subtopic: Β Different Types of AC Circuits |
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An inductor of \(10~\text{mH}\), capacitor of \(0.1 ~\mu \text{F}\) and a resistor of \(100~\Omega\)
1. \(100\)
2. \(300\)
3. \(500\)
4. \(600\)
1. \(100\)
2. \(300\)
3. \(500\)
4. \(600\)
Subtopic: Β Power factor |
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A capacitor \(C\) is first charged fully with potential difference of \(V_0\) and disconnected from the battery. The charged capacitor is connected across an inductor having inductance \(L\). In \(t\) s \(25\%\) of the initial energy in the capacitor is transferred to the inductor. The value of \(t\) is: (in s)
1. \(\dfrac{\pi \sqrt{{LC}}}{3}\)
2. \(\dfrac{\pi \sqrt{{LC}}}{6}\)
3. \(\dfrac{\pi \sqrt{{LC}}}{2}\)
4. \(\pi \sqrt{\dfrac{{LC}}{2}}\)
1. \(\dfrac{\pi \sqrt{{LC}}}{3}\)
2. \(\dfrac{\pi \sqrt{{LC}}}{6}\)
3. \(\dfrac{\pi \sqrt{{LC}}}{2}\)
4. \(\pi \sqrt{\dfrac{{LC}}{2}}\)
Subtopic: Β Different Types of AC Circuits |
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Figure shows the circuit that contains three resistances (\(9~\Omega\) each) and two inductors (\(4~\text{mH}\) each). The reading of ammeter at the moment switch \(K\) is turned ON, is: (in \(\text{A}\))
1. \(1\)
2. Zero
3. \(3\)
4. \(2\)
1. \(1\)
2. Zero
3. \(3\)
4. \(2\)
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Using a variable-frequency a.c. voltage source, the maximum current measured in the given \(LCR\) circuit is \(50~\text{mA}\) for \(V = 5\sin(100t)\). The values of \(L\) and \(R\) are shown in the figure. The capacitance of the capacitor \((C)\) used is: (in \(\mu\text{F}\))
1. \(50\)
2. \(20\)
3. \(30\)
4. \(40\)
1. \(50\)
2. \(20\)
3. \(30\)
4. \(40\)
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For the series \(\text L\text C\text R\) circuit connected with \(220~\text V \), \(50~\text{Hz}~\text {a.c}\) source as shown in the figure, the power factor is \(\dfrac{a}{10}.\) The value of \(a\) is:
1. \(4\)
2. \(10\)
3. \(6\)
4. \(8\)
1. \(4\)
2. \(10\)
3. \(6\)
4. \(8\)
Subtopic: Β Power factor |
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