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In which of the following cases is the RMS voltage equal to the maximum voltage in magnitude?
(A)
(B)
(C)
1. A
2. A, B
3. A, B, C
4. None of the above

Subtopic:  RMS & Average Values |
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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. \(90^{\circ}\)
Subtopic:  Different Types of AC Circuits |
From NCERT
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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 |
From NCERT
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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 |
 52%
From NCERT
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An alternating emf of  \(V=20\) V \(\mathrm{sin}(100\pi ~\text{s}^{-1}.t)\) is applied to an inductor and the peak current through the inductor is observed to be \(\dfrac{20}{\pi}\) A. The inductance is:
1. \(\dfrac{1}{10}\) H 2. \(\dfrac{1}{100}\) H
3. \(\dfrac{1}{1000}\) H 4. \(\dfrac{1}{10^4}\) H
Subtopic:  RMS & Average Values |
 85%
From NCERT
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A household ac circuit has an applied voltage of \(220\) V (RMS) and the current flowing through the circuit is \(2.2\) A (RMS), the phase difference between them being \(60^\circ.\) Then:
1. the impedance in the circuit is \(100~\Omega.\)
2. the resistance in the circuit is \(200~\Omega.\)
3. the power dissipated is \(484\) W.
4. all the above are true.
Subtopic:  Different Types of AC Circuits |
 64%
From NCERT
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In this \(LCR\) circuit, it is observed that the current and the voltage are in phase with each other. When the capacitor is replaced by a short circuit, the phase difference becomes \(60^{\circ}.\)

Then:
1. \(\dfrac{L}{C}=R^2 \) 2. \(\dfrac{L}{C}=2R^2\)
3. \(\dfrac{L}{C}=3R^2\) 4. \(\dfrac{L}{C}=\dfrac13R^2\)
Subtopic:  Different Types of AC Circuits |
 65%
From NCERT
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An alternating emf (AC) is applied across the circuit shown in the figure. Let \(V_{AX}\) be the voltage across the inductor \(L,\) and \(V_{XY}\) be the voltage across the resistor \(R.\) Let the angular frequency be \(\omega.\) The phase difference between \(V_{XY}\) and \(V_{AX}\):
                 
1. depends on the ratio \(\dfrac{\omega L}{R}\)
2. depends on the quantity \(\sqrt{(\omega L)^2+R^2}\)
3. depends on \(L\) and \(R,\) but not on \(\omega\)
4. is independent of \(L,R,\omega\)
Subtopic:  Different Types of AC Circuits |
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Two circuits: \((1)\) an \(L\text-R\) circuit and \((2)\) an \(R\text-C\) circuit are driven by the same alternating current. The phase difference between the current and the voltage is twice in the \(1\)st case with respect to the \(2\)nd case and both the angles add up to \(90^\circ.\) The resistances are equal in both cases. The ratio of their reactances (first: second) is:
1. \(\sqrt3:1\) 2. \(1:\sqrt3\)
3. \(3:1\) 4. \(2:1\)
Subtopic:  Different Types of AC Circuits |
 53%
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An AC source of emf \(100~\text{V}\) and frequency \(f= \dfrac{50}{\pi}\) Hz has an internal resistance \(100~\Omega\). A load resistance \(R_L\) is connected across the source. Maximum power is dissipated in the load, when: 
1. \(R_L = 100\sqrt 2~\Omega\) 2. \(R_L = \dfrac{100}{\sqrt 2}~\Omega \)
3. \(R_L = 100~\Omega\) 4. \(R_L = 200~\Omega\)
Subtopic:  Different Types of AC Circuits |
 68%
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