Q 11 :

In an LCR series circuit, an inductor 30 mH and a resistor 1 $\Omega$ are connected to an AC source of angular frequency 300 rad/s. The value of capacitance for which the current leads the voltage by $45°$ is $\frac{1}{x}\times {10}^{-3}\text{\hspace{0.05em}F}$. Then the value of $x$ is _______.

Q 12 :

In the circuit shown below, what will be the reading of the voltmeter and ammeter?

• 800 V, 2A

   

• 300 V, 2A

   

• 220 V, 2.2A

   

• 0 V,1A

   

Q 13 :

A source of alternating emf $E=E_0\sin \omega t$ is connected in series with a capacitor and inductor in a circuit with negligible resistance. Natural frequency of $LC$ oscillation is ${\omega }_0=\frac{1}{\sqrt{LC}}$. If charge on capacitor at any moment is given by $Q=Q_0\sin \omega t$ then magnitude of $Q_0$ is:

• $\frac{E_0}{|{\omega }^2-{\omega }_0^2|}$

   

• $\frac{E_0}{L{\omega }^2}$

   

• $\frac{E_0}{L|{\omega }^2-{\omega }_0^2|}$

   

• $\frac{E_0}{L{\omega }_0^2}$

   

Q 14 :

Assertion A : In series LCR circuit, resonance can take place.

Reason R : Resonance takes place if inductive and capacitive reactances are not equal.

• A is false but R is true

   

• A is true but R is false

   

• Both A and R are true and R is the correct explanation of A

   

• Both A and R are true but R is NOT the correct explanation of A

   

Q 15 :

An inductor of 10 mH, capacitor of $0.1\mu \mathrm{F}$ and a resistor of $100\Omega$ are connected in series across an a.c. power supply 220 V, 70 Hz. The power factor of the given circuit is 0.5. The difference in the inductive reactance and capacitance reactance is $\sqrt{3}\alpha \Omega$. The value of $\alpha$ is ______.             [2026]

Q 16 :

A series LCR circuit with R = 20 $\mathrm{\Omega }$, L = 1.6 H and C = 40 $\mathrm{\mu F}$ is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is _____ $\mathrm{\Omega }$.    [2026]