\(L,C\) and \(R\) represent the value of inductance, capacitance and resistance, respectively. The factor which has the same dimensions as that of the inverse of resonance frequency is:
1. \(\sqrt{LC}\)
2. \(\sqrt{\dfrac{L}{C}}\)
3. \(\dfrac{C}{L}\)
4. \(\dfrac{R}{L}\)
Subtopic:  Different Types of AC Circuits |
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In the circuit shown below, the inductance \(L\) is connected to a source. The current flowing in the circuit is \({I=I_{0}\sin\omega t.}\) The voltage drop \((V_L)\) across \(L\) is:

1. \(\omega L~I_0\sin\omega t\)
2. \(\frac{{I}_0}{\omega{L}}\sin\omega t\)
3. \(\frac{{I}_0}{\omega{L}}\cos\omega t\)
4. \(\omega L~I_0\cos\omega t\)
Subtopic:  Different Types of AC Circuits |
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An ac source is connected to a capacitor \(C\). Due to decrease in its operating frequency:
1. capacitive reactance remains constant
2. capacitive reactance decreases.
3. displacement current increases.
4. displacement current decreases.
Subtopic:  Different Types of AC Circuits |
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In a series \({LCR}\) circuit, the inductance \({L}\) is \(10~\text{mH}\), capacitance \({C}\) is \(1~\mu\text{F}\) and resistance \({R}\) is \(100~\Omega\). The frequency at which resonance occurs is:
1. \(1.59~\text{kHz}\) 2. \(15.9~\text{rad/s}\)
3. \(15.9~\text{kHz}\) 4. \(1.59~\text{rad/s}\)
Subtopic:  Different Types of AC Circuits |
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The net impedance of circuit (as shown in the figure) will be:

1. \(25~\Omega\)
2. \(10\sqrt{2}~\Omega\)
3. \(15~\Omega\)
4. \(5\sqrt{5}~\Omega\)
Subtopic:  Different Types of AC Circuits |
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An AC source is connected to the given circuit. The value of \(\phi\) will be:
1. \(60^\circ\) 2. \(90^\circ\)
3. \(30^\circ\) 4. \(45^\circ\)
Subtopic:  Different Types of AC Circuits |
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If \(Z_1\) and \(Z_2\) are the impedances of the given circuits (a) and (b) as shown in figures, then choose the correct option:
         
1. \(Z_1<Z_2\) 2. \(Z_1+Z_2=20~\Omega\)
3. \(Z_1=Z_2\) 4. \(Z_1>Z_2\)
Subtopic:  Different Types of AC Circuits |
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For very high frequencies, the effective impedance of the circuit (shown in the figure) will be: 
1. \(4~ \Omega\) 2. \(6~ \Omega\)
3. \(1~ \Omega\) 4. \(3~ \Omega\)
Subtopic:  Different Types of AC Circuits |
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A series \(LCR\) circuit with inductance \(10~\text{H}\), capacitance \(10~\mu \text{F}\), resistance \(50~\Omega\) is connected to an AC source of voltage, \(V=200 \sin (100 t) \text { volt }\). If the resonant frequency of the \(LCR\) circuit is \(\nu_0\) and the frequency of the AC source is \(\nu\), then:
1. \(\nu=100 ~\text{Hz} ; ~\nu_0=\dfrac{100}{\pi} ~\text{Hz}\)
2. \(\nu_0=\nu=50~\text{Hz}\)
3. \(\nu_0=\nu=\dfrac{50}{\pi} ~\text{Hz}\)
4. \(\nu_{0}=\dfrac{50}{\pi}~ \text{Hz}, \nu=50 ~\text{Hz}\)
Subtopic:  Different Types of AC Circuits |
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Given below are two statements:
Statement I: In an AC circuit, the current through a capacitor leads the voltage across it.
Statement II: In AC circuits containing pure capacitance only, the phase difference between the current and the voltage is \(\pi.\)
 
1. Both Statement I and Statement II are correct.
2. Both Statement I and Statement II are incorrect.
3. Statement I is correct but Statement II is incorrect.
4. Statement I is incorrect but Statement II is correct.
Subtopic:  Different Types of AC Circuits |
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