Resonance in RLC Circuit

Q.

A tube closed at one end and containing air produces, when excited, the fundamental note of frequency 512 Hz. If the tube is open at both ends the fundamental frequency that can be excited is ( in Hz ):

1. 512

2. 128

3. 256

4. 1024

Q. An open pipe resonates to frequency f1 and a closed pipe resonates to a frequency f2 if they are joined together to form a longer tube then it will resonate to a frequency of (neglect end corrections)

Q. nta particle executes SHM with frequency 4Hz . Frequency with which its PE oscillates isn

Q. 91.The frequency of the first overtone of an open organ pipe is f. Find the frequency of first overtone of the closed organ pipe of same length.

Q. 135.An organ pipe closed at one end has fundamental frequency of 1500Hz. The maximum number of overtones generated by this pipe which a normal person can hear is 1) 14 2) 13 3) 6 4) 9

Q. 98.If n1, n2, and n3 are the fundamental frequency of three segment into which a string is divided then the original fundamental frequency n of the sting is?

Q. In $L-R$ circuit shown in diagram, reading of ammeter is $i_1$. Now, a diamagnetic material is inserted into the inductor, then the new reading of ammeter is $i_2,$ will be

1. $i_1>i_2$
2. $i_2>i_1$
3. $i_1=i_2$
4. cannot say about $i_{1}and{i}_2,$ it depends upon value of R

Q. In a LCR circuit having L = 8.0 henry, $C=0.5\mu F$ and R = 100 ohm in series. The resonance frequency in per second is

1. 600 radian per sec
2. 600 Hz
3. 500 radian per sec
4. 500 Hz

Q. 4.Frequency of oscillation of a body is 6Hz when F1 is applied and 8Hz when F2 is applied. if both forces F1 and F2 are applied together then find out the frequency of oscillation?

Q. 12.A source of frequency f gives 5 beats per second when sounded with a source of frequency 200hz. The second harmonic of frequency 2f of source gives 10 beats per second when sounded with a source of frequency 420hz. The value of f is

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. the fundamental frequency of a string stretched with a weight of 4kg is 256 Hz. the weight required to produce its octave is? (ans :16 kg wt)

Q. For an $LCR$ circuit, resonance frequency is ${\omega }_o$ and bandwidth is $△\omega$, then

1. circuit is inductive for $({\omega }_o-\frac{△\omega }{2})$
2. circuit is capacitive for $({\omega }_o+\frac{△\omega }{2})$
3. circuit is resistive for $({\omega }_o-\frac{△\omega }{2})$
4. circuit is inductive for $({\omega }_o+\frac{△\omega }{2})$

Q. What is the peak voltage across capacitor at resonance frequency in the given circuit ?

1. $100V$
2. $10V$
3. $5V$
4. $50V$

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. In the series $LCR$ circuit shown, the readings of voltmeter and ammeter respectively are

1. $V=100\text{V};I=2\text{A}$
2. $V=300\text{V};I=1\text{A}$
3. $V=1000\text{V};I=2\text{A}$
4. $V=100\text{V};I=5\text{A}$

Q. A circuit of resistance $5\Omega$ and inductance $0.6H$ is in series with a capacitance of $10\mu F$. If a voltage of $200\text{V}$ is applied and the frequency is adjusted to resonance. The current in the circuit is $I_0$ and voltage across the inductor and capacitor are $V_0$, and $V_1$ respectively. We have

1. $I_0=40A$
2. $V_0=9.8kV$
3. $V_1=9.8kV$
4. $V_1=19.6kV$

Q. The values of $L$ and $R$ in $LCR$ circuit are $1mH$ and $10\Omega$ respectively. What is the value of its bandwidth?

1. $\frac{10000}{2\pi }Hz$
2. $\frac{1000}{\sqrt{3}}Hz$
3. $\frac{100}{\pi }Hz$
4. $\frac{100}{\sqrt{2}}Hz$