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Q. No.Sinusoidal voltages are applied at \(X\) and \(Y\) so that the currents flowing into the capacitor at \(X\) and into the resistor at \(Y\) are equal and out of phase with each other. The RMS values of the voltages across the capacitor and the resistor are each equal to \(V_r\). The RMS value of \(V_X-V_Y\) is:
1.
zero
2.
\(\sqrt 2 V_r \)
3.
\(2 V_r\)
4.
\(\dfrac{V_r}{\sqrt 2}\)
Subtopic: Different Types of AC Circuits |
Level 3: 35%-60%
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An alternating \(\text{emf}= V_0\sin \omega t\) is applied between the two ends \(A\) & \(B\) of the circuit shown below. The current through \(C\) has the same RMS value as that through \(R.\) The RMS value of the current flowing out at \(B\) is:
1. \(\dfrac{V_0}{ \sqrt 2 R}\)
2. \(\dfrac{V_0}{ R}\)
3. \(\dfrac{ \sqrt 2 V_0}{R}\)
4. zero
1. \(\dfrac{V_0}{ \sqrt 2 R}\)
2. \(\dfrac{V_0}{ R}\)
3. \(\dfrac{ \sqrt 2 V_0}{R}\)
4. zero
Subtopic: Different Types of AC Circuits |
Level 3: 35%-60%
Please attempt this question first.
Hints
The RMS voltage across the inductor is twice that across the capacitor, while the applied RMS voltage across the entire combination (i.e. \(V_{AX}\)) is \(V_r\). The RMS voltage across the capacitor is:
| 1. | \(\dfrac{V_r}{3}\) | 2. | \(\dfrac{2V_r}{3}\) |
| 3. | \(\dfrac{V_r}{2}\) | 4. | \(V_r\) |
Subtopic: Different Types of AC Circuits |
52%
Level 3: 35%-60%
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Exactly identical voltages are imposed on the system at \(X, Y,\) and \(Z:V_m \sin \omega t\). The peak voltage at \(O\) is \(V_o\). Then:
1. \(V_o = V_m\)
2. \(V_o < V_m \)
3. \(V_o > V_m\)
4. any of the above can be possible.
1. \(V_o = V_m\)
2. \(V_o < V_m \)
3. \(V_o > V_m\)
4. any of the above can be possible.
Subtopic: Different Types of AC Circuits |
54%
Level 3: 35%-60%
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An \(RC\) circuit is connected to a \(10\) V AC source and it is observed to supply a \(200\) mA current at a frequency of \(100\) kHz. The same resistance is now paired with an inductor \((L)\) in series and the same source supplies \(200\) mA current at a frequency of \(1\) kHz at the same operating voltage. If the circuit were made with the given \(L\text-C\text-R\) in series, the current will be a maximum when the frequency is \(f_o\). Then,
| 1. | \(f_o = \dfrac{10^3 + 10^5}{2}\) Hz |
| 2. | \(f_o > \dfrac{10^3 + 10^5}{2}\) Hz |
| 3. | \(f_o < \dfrac{10^3 + 10^5}{2}\) Hz |
| 4. | \(f_o = {10^3 + 10^5}\) Hz |
Subtopic: Different Types of AC Circuits |
Level 3: 35%-60%
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The end \('B'\) of the circuit is earthed \((V_B = 0)\) while a sinusoidal voltage is applied at \('A';\) \(V_{A}=V_{0} \sin \omega t.\) The rms voltage across the capacitor \({C}\) equals that across the upper resistor \({R}\) (as shown in the figure). What is the phase difference between the current through the capacitor and the voltage across the capacitor when no current flows out at \(X?\)
| 1. | \(0^{\circ}\) | 2. | \(45^{\circ}\) |
| 3. | \(90^{\circ}\) | 4. | \(180^{\circ}\) |
Subtopic: Different Types of AC Circuits |
61%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
In which of the following cases is the RMS voltage equal to the maximum voltage in magnitude?
1. A
2. A, B
3. A, B, C
4. None of the above
| (A) |  |
| (B) |  |
| (C) |  |
2. A, B
3. A, B, C
4. None of the above
Subtopic: RMS & Average Values |
51%
Level 3: 35%-60%
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In an \(\text{AC}\) circuit, the power dissipated in a resistance is found to \(P_1\) when a source voltage of \(V_1\) is connected across it. If the same resistance is connected in series with a capacitance and the same source is connected across the combination, the power in the resistance is found to be \(P_2=\dfrac{P_1}{2}.\) The phase difference between the voltage and the current is:
1. \(30^{\circ}\)
2. \(60^{\circ}\)
3. \(45^{\circ}\)
4. \(90^{\circ}\)
1. \(30^{\circ}\)
2. \(60^{\circ}\)
3. \(45^{\circ}\)
4. \(90^{\circ}\)
Subtopic: Different Types of AC Circuits |
Level 3: 35%-60%
Hints
An alternating current given by \(I=I_0~\sin\omega t+I_0~\cos\omega t\) flows through a circuit. The RMS current is:
| 1. | \(I_0\) | 2. | \(\dfrac{I_0}{\sqrt2}\) |
| 3. | \(\sqrt2I_0\) | 4. | zero |
Subtopic: RMS & Average Values |
51%
Level 3: 35%-60%
Hints
The primary has \(100\) turns with \(100\) V RMS applied to it while the secondary has a total number of \(20\) turns, with the connection \(C\) made at the centre. The current \(i\) flowing towards \(C\) has the (RMS) value:
| 1. | \(2\) A | 2. | \(2\sqrt2\) A |
| 3. | \(\sqrt2\) A | 4. | zero |
Subtopic: Transformer |
54%
Level 3: 35%-60%
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