Q 21 :

A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains a resistance $R=8\Omega$, an inductor of inductive reactance $X_L=70\Omega$, and a capacitor of capacitive reactance $X_C=130\Omega$. The power factor of the circuit is $\frac{x}{10}$. The value of $x$ is _________.            [2023]
 

Q 22 :

A series LCR circuit consists of $R=80\Omega$, $X_L=100\Omega$ and $X_C=40\Omega$. The input voltage is $2500\cos \left(100\pi t\right)\text{\hspace{0.05em}V}$. The amplitude of current in the circuit is ______ A.       [2023]

Q 23 :

A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains a resistance $R=100\Omega$ and an inductor of inductive reactance $X_L=79.6\Omega$. The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be _________ $\text{μF}$.              [2023]

Q 24 :

An inductor of inductance $2\mu \text{H}$ is connected in series with a resistance, a variable capacitor and an AC source of frequency 7 kHz. The value of capacitance for which maximum current is drawn into the circuit is $\frac{1}{x}\text{F}$, where the value of $x$ is _______. (Take $\pi =\frac{22}{7}$)                 [2023]
 

Q 25 :

An inductor of 0.5 mH, a capacitor of $20\mu \text{F}$ and a resistance of $20\Omega$ are connected in series with a 220 V AC source. If the current is in phase with the emf, the amplitude of current of the circuit is $\sqrt{x}\text{A}$. The value of $x$ is _______.            [2023]

Q 26 :

A series combination of a resistor of resistance $100\Omega$, an inductor of inductance 1 H and a capacitor of capacitance $6.25\mu \text{F}$ is connected to an AC source. The quality factor of the circuit will be ________.            [2023]

Q 27 :

Using a variable frequency a.c. voltage source the maximum current measured in the given LCR circuit is 50 mA for V = 5sin(100t). The values of L and R are shown in the figure. The capacitance of the capacitor (C) used is ______ $\mu F$.                 [2026]

Q 28 :

For the series LCR circuit connected with 220 V, 50 Hz a.c. source as shown in the figure, the power factor is $\frac{\alpha }{10}$. The value of $\alpha$ is ________.         [2026]

• 10

   

• 4

   

• 8

   

• 6

   

Q 29 :

Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a $I=10\sin \left(\omega t\right) \text{A}, \text{where }\omega =1000 \text{rad/s}.$ A circular conducting loop (B) of radius 1 cm coaxially slides through the solenoid at speed v=1 cm/s. The r.m.s. current through the loop when the coil B is inserted 10 cm inside the solenoid is $\frac{\alpha }{\sqrt{2}} \mu \text{A}$. The value of $\alpha$ is ______.

[Resistance of the loop =$10 \Omega$]    [2026]

• 280

   

• 80

   

• 197

   

• 100

   

Q 30 :

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 ts, 25% of the initial energy in the capacitor is transferred to the inductor. The value of t is ________ s.   [2026]

• $\frac{\pi \sqrt{LC}}{2}$

   

• $\pi \sqrt{\frac{LC}{2}}$

   

• $\frac{\pi \sqrt{LC}}{3}$

   

• $\frac{\pi \sqrt{LC}}{6}$