Resonance in RLC Circuit

Q. Ten tuning forks are arranged in increasing order of frequency in such a way that any two nearest tuning forks produce 4 beats/sec. The highest frequency is twice of the lowest. Possible highest and the lowest frequencies are

1. 80 and 40
2. 100 and 50
3. 44 and 22
4. 72 and 36

Q. A box containing a resistance $R$, inductance $L$ and a capacitor of capacitance $C$ is connected in series to an alternating source of angular frequency $4rad/s$ and a capacitor of capacitance $C$ as shown in the circuit. Box has power factor of $\frac{1}{\sqrt{3}}$ and the circuit has overall power factor of $1$. The impedance of the box is

1. $\frac{1}{4C}$
2. $\frac{3}{4\sqrt{2}C}$
3. $\frac{\sqrt{3}}{4\sqrt{2}C}$
4. $\frac{1}{4\sqrt{2}C}$

Q.

Find the peak current and resonant frequency of the following circuit (as shown in the figure)

1. $0.2A$and $100Hz$

2. $2A$and $50Hz$

3. $2A$and $100Hz$

4. $0.2A$and $50Hz$

Q. 25.A coil of self inductance L is connected in series with a bulb B and AC source. Brightness of the bulb decreases when 1)Number of turns in the coil is reduced 2)capacitance of reactance Xl=Xc is included in same circuit 3) Iron Rod is inserted in the coil. 4) Frequency of AC source is decreased

Q. The amplifiers A, B and C are connected in series. If the voltage gain of A, B and C are 10, 15 and 20 respectively and input signal 2 mV peak value. Then the output signal voltage’s peak value will be (1) 6 V(2) 5 V(3) 3 V (4) 4 V

Q. In a series $LCR$ circuit, the inductance, capacitance and resistance are $L=100mH,C=100\mu F$ and $R=10\Omega$ respectively. They are connected to an $AC$ source of voltage $220V$ and frequency of $50Hz$. The approximate value of current in the circuit will be $A$.

Q.

What is a series resonance circuit?

Q. To increase the resonant frequency in series $LCR$ circuit,

1. Source frequency should be increased.
2. Another resistance should be added in series with the first resistance.
3. Another capacitor should be added in series with the first capacitor.
4. The source frequency should be decreased.

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

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. As shown in the figure an inductor of inductance $200mH$ is connected to an AC source of emf $220\text{V}$ and frequency $50\text{Hz}$. The instantaneous voltage of the source is $0\text{V}$ when the peak value of current is $\frac{\sqrt{a}}{\pi }\text{A}$. The value of $a$ is

Q.

What is the unit of Capacitive Reactance X_c?

1. mhO

2. Ohm

3. Ohm^-1

4. Ohm²

Q. A transistor is used as an amplifier in $CB-$ mode with a load resistance of $5k\Omega$ the current gain of amplifier is $0.98$ and the input resistance is $70\Omega .$ The voltage gain and power gain respectively are

1. $70;68.6$
2. $80;75.6$
3. $60;66.6$
4. $90;96.6$

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

Q. In a series $CR$ circuit shown in figure, the applied voltage is $10V$ and the voltage across capacitor is found to be $8V$. Then the voltage across $R$, and the phase difference between current and the applied voltage will respectively be

1. $6V,{\tan }^{-1}\left(\frac{4}{3}\right)$
2. $3V,{\tan }^{-1}\left(\frac{3}{4}\right)$
3. $6V,{\tan }^{-1}\left(\frac{5}{3}\right)$
4. Zero, Zero

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

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

Q. 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.

If an emitter current is changed by $4mA$, the collector current changes by $3.5mA$. The value of $\beta$ will be:

1. $7$

2. $0.875$

3. $0.5$

4. $3.5$

Q.

R, L and C represent the physical quantities resistance, inductance and capacitance, respectively. Which one of the following combinations has the dimension of frequency?

1. $\frac{1}{\sqrt{RC}}$

2. $\frac{R}{L}$

3. $\frac{1}{LC}$

4. $\frac{C}{L}$

Q.

The maximum resistance which can be made using four resistors each of $2\Omega$ is

1. $2\Omega$

2. $4\Omega$

3. $8\Omega$

4. $16\Omega$

Q. An inductor of inductance 100mH is connected in series with a resistance, a variable capacitance and an AC source of frequency 2.0 kHz. The value of the capacitance so that maximum current may be drawn into the circuit.

1. 60 nF
2. 63 nF
3. 50 nF
4. 79 nF

Q. In a series circuit $C=2\mu F,L=1mHandR=10\Omega$, when the current in the circuit is maximum, at that time the ratio of the energies stored in the capacitor and the inductor will be

1. 1 : 1
2. 1 : 2
3. 2 : 1
4. 1 : 5

Q. A uniform wire of length L and mass M is stretched between two fixed points, keeping a tension F.A sound of frequency is impressed on it.Then the maximum vibrational energy is existing in the wire whenis equal to

Q. In the circuit shown, the input waveform is given. Which of the following correctly gives the output waveform across RL?

Q. For an a-c circuit containing inductor only as shown. The graph of inductive reactance (XL) vs frequency f of an ac

Q. The figure show a series LCR circuit with $L=5.0H,C=80\mu F,R=40\Omega$ connected to variable frequency 240 V source. Calculate
(i)The angular frequency of the source which driver the circuit at resonance
(ii) The current at the frequency.
(iii)The rms potential drop across the capacitor at resonance

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.

What is the natural frequency of an LC oscillator?

1. 

2. 

3. 

4. 

Q. 16. For the series LCR circuit shown , what is the resonance frequency and the amplitude of the current at the resonating frequency

Q. Assertion : Eddy currents heat up the core and dissipate electrical energy in the form of heat.

Reason : Eddy currents are always undesirable.

Choose the correct alternative corresponding to the given assertion and reason.

1. Both assertion and reason are correct, and reason is the correct explanation of the assertion
2. Both assertion and reason are correct, and reason is not the correct explanation of the assertion
3. Assertion is correct, but reason is incorrect
4. Assertion is incorrect, but reason is correct