Resonance in RLC Circuit

Q.

What are the two requirements for oscillation?

Q.

A resonance circuit having inductance and resistance $2\times {10}^{–4}H$ and $6.28\Omega$ respectively oscillates at $10MHz$ frequency. The value of the quality factor of this resonator is________. [$\pi =3.14$]

Q. A series LCR circuit containing a resistor of $120\Omega$ has an angular resonant frequency $4\times {10}^{5}rad{s}^{-1}$. At resonance the voltages across resistor and inductor are $60\text{V}$ and $40\text{V}$ respectively.
At what frequency, the current in the circuit lags the voltage by ${45}^{\circ }$?

1. $4\times {10}^{5}rad{s}^{-1}$
2. $3\times {10}^{5}rad{s}^{-1}$
3. $8\times {10}^{5}rad{s}^{-1}$
4. $2\times {10}^{5}rad{s}^{-1}$

Q. An ac circuit consists of an inductor of inductance 0.5 H and a capacitor of capacitance $8\mu F$ in series. The current in the circuit is maximum when the angular frequency of ac source is

1. 500 rad/sec
2. $2\times {10}^{5}rad/sec$
3. 4000 rad/sec
4. 5000 rad/sec

Q. The inductance L (in mH) of the coil which is to be connected in series with a capacitor of 0.3 pF to get an oscillatory resonance frequency of 1 MHz is.

1. 8.44mH
2. 84.4mH
3. 844mH
4. 8440mH

Q. A series L-C-R circuit with R = 20 $\Omega$ L = 1.5 H and C = 35$\mu$ F is connected to a variable frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit, the average power transferred to the circuit in one complete cycle is

1. 0.5 KW
2. 1.0 KW
3. 2.0 KW
4. 4.0 KW

Q. A resistance of 10 $\Omega$ capacitance of 0.1$\mu$F and an inductance of 2mH are connected in series across source of alternating emf of variable frequency. At that frequency does maximum current flow?

1. 11.25 kHz
2. 23.76 kHz
3. 35.46 kHz
4. 46.72 kHz

Q. A series LCR circuit has L = 1mH, C = 0.1 $\mu$F and R = 10 $\Omega$ . It is connected across a source of alternating emf of 5V but of variable frequency. Find (i) the frequency at which the impedance is minimum (ii) the current at resonance.

1. $\frac{{10}^5}{2\pi }Hz,\frac{1}{2}A$
2. $\frac{{10}^4}{2\pi }Hz,\frac{1}{2}A$
3. $\frac{{10}^2}{2\pi }Hz,\frac{1}{2}A$
4. $\frac{{10}^3}{2\pi }Hz,\frac{1}{2}A$

Q. A series L-C-R circuit with R = 20 $\Omega$ L = 1.5 H and C = 35$\mu$ F is connected to a variable frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit, the average power transferred to the circuit in one complete cycle is

1. 0.5 KW
2. 1.0 KW
3. 2.0 KW
4. 4.0 KW