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In an \( LCR \) series circuit, an inductor \( 30 \, \text{mH} \) and a resistor \( 1 \, \Omega \) are connected to an AC source of angular frequency \( 300 \, \text{rad/s} \). The value of capacitance for which, the current leads the voltage by \( 45^\circ \) is \( \dfrac{1}{x} \times 10^{-3} \, \text{F} \). Then the value of \( x \) is ___________.

A \( 100 \, \Omega \) resistance, a \( 0.1 \, \mu \text{F} \) capacitor and an inductor are connected in series across a \( 250 \, \text{V} \) supply at variable frequency. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant frequency is \( 60 \, \text{Hz} \).

Match List-I with List-II:

List-I	List-II
(a) Phase difference between current and voltage in a purely resistive AC circuit	(i) \( \dfrac{\pi}{2} \); current leads voltage
(b) Phase difference between current and voltage in a pure inductive AC circuit	(ii) Zero
(c) Phase difference between current and voltage in a pure capacitive AC Circuit	(iii) \( \dfrac{\pi}{2} \); current lags voltage
(d) Phase difference between current and voltage in an LCR series circuit	(iv) \( \tan^{-1}\!\left(\frac{X_C - X_L}{R}\right) \)

Choose the most appropriate answer from the options given below:

What happens to the inductive reactance and the current in a purely inductive circuit if the frequency is halved?

In a series LCR resonance circuit, if we change the resistance only, from a lower to higher value:

An ac circuit has an inductor and a resistor of resistance \( R \) in series, such that \( X_L = 3R \). Now, a capacitor is added in series such that \( X_C = 2R \). The ratio of new power factor with the old power factor of the circuit is \( \sqrt{5} : x \). The value of \( x \) is ________.

Two circuits are shown in the figure (a) & (h). At a frequency of ______ \( \text{rad /s} \) the average power dissipated in one cycle will be same in both the circuits.

An AC source rated \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) is connected to a resistor. The time taken by the current to change from its maximum to the rms value is:

In a series LCR circuit, the inductive reactance \( (X_L) \) is \( 10 \, \Omega \) and the capacitive reactance \( (X_C) \) is \( 4 \, \Omega \). The resistance \( (R) \) in the circuit is \( 6 \, \Omega \). The power factor of the circuit is:

10.

Intensity of sunlight is observed as \( 0.092 \, \mathrm{W \, m^{-2}} \) at a point in free space. What will be the peak value of magnetic field at the point? \(( \varepsilon_{0} = 8.85 \times 10^{-12} \, \mathrm{C^{2} \, N^{-1} \, m^{-2}}) \)

11.

In a circuit consisting of a capacitance and a generator with alternating emf \( E_g = E_g \sin \omega t \), \( V_c \) and \( I_c \) are the voltage and current. Correct phasor diagram for such circuit is:

12.

A \( 0.07 \, \text{H} \) inductor and a \( 12 \, \Omega \) resistor are correct in series to a \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) ac source. The approximate current in the circuit and the phase angle between current and source voltage are respectively. \([\text{Take } \pi \text{ as } \tfrac{22}{7}]\)

13.

A series LCR circuit is designed to resonate at an angular frequency \( \omega_{0}=10^{5} \, \text{rad/s} \). The circuit draws \( 16 \, \text{W} \) power from \( 120 \, \text{V} \) source at resonance. The value of resistance ‘\( R \)’ in the circuit is ________ \( \Omega \).

14.

A series \( LCR \) circuit driven by \( 300 \, \text{V} \) at a frequency of \( 50 \, \text{Hz} \) contains a resistance \( R = 3 \, \text{k}\Omega \), an inductor of inductive reactance \( X_L = 250\pi \, \Omega \) and an unknown capacitor. The value of capacitance to maximize the average power should be: (Take \( \pi^2 = 10 \) )

15.

At very high frequencies, the effective impedance of the given circuit will be ______ \( \Omega \) .

16.

A \( 10\,\Omega \) resistance is connected across \( 220 \, \text{V} \) - \( 50 \, \text{Hz} \) AC supply. The time taken by the current to change from its maximum value to the rms value is:

17.

The alternating current is given by
\( i = \left( \sqrt{42} \sin\!\left( \dfrac{2\pi}{T} t \right) + 10 \right) \, \text{A} \).
The r.m.s. value of this current is__________ \( \text{A} \).

18.

In the given circuit the AC source has \( \omega = 100 \, \text{rad} \, \text{s}^{-1} \). Considering the inductor and capacitor to be ideal, what will be the current \( I \) flowing through the circuit?

19.

A series LCR circuit of \( R = 5 \Omega \), \( L = 20 \, \text{mH} \) and \( C = 0.5 \, \mu \text{F} \) is connected across an AC supply of \( 250 \, \text{V} \), having variable frequency. The power dissipated at resonance condition is ______________ \( \times 10^{2} \, \text{W} \) .

20.

AC voltage \( V(t) = 20 \sin \omega t \) of frequency \( 50 \, \text{Hz} \) is applied to a parallel plate capacitor. The separation between the plates is \( 2 \, \text{mm} \) and the area is \( 1 \, \text{m}^2 \). The amplitude of the oscillating displacement current for the applied AC voltage is ________.

21.

An AC current is given by \( I = I_1 \sin \omega t + I_2 \cos \omega t \). A hot wire ammeter will give a reading:

22.

Match List-I with List-II:

Choose the correct answer from the options given below:

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JEE Mains JEE Advance BITSAT
JEE Mains | PYQ