Frequency of Oscillations in LC Circuit

Q.

Obtain the equivalent capacitance of the network in Fig. 2.35. For a 300 V supply, determine the charge and voltage across each capacitor.

Q. 29.Two capacitors C1 and C2 of unknown capacitance are connected first in series and then in parallel across a battery of 100V. If the energy stored in the 2 combinations is 0.045J and 0.25J respectively, determine the values of C1 and C2. Also determine the charge on each capacitors in parallel combination

Q.

A capacitor of capacitance 1 μF is charged to a potential of 1 V. It is connected in parallel to an inductor of inductance 10^-3 H. The maximum current that will flow in the circuit has the value

1. 
   

2. 1 mA

3. 1 μF

4. 1000 mA

Q. A series $\text{AC}$ circuit containing an inductor $\left(20\text{mH}\right)$, a capacitor $\left(120\mu \text{F}\right)$ and a resistor $\left(60\Omega \right)$ is driven by an $\text{AC}$ source of $24\text{V},50\text{Hz}$. The energy dissipated in the circuit in $60\text{sec}$ is:

1. $5.65\times {10}^2\text{J}$
2. $2.26\times {10}^3\text{J}$
3. $5.17\times {10}^2\text{J}$
4. $3.39\times {10}^3\text{J}$

Q.
In the above circuit, $C=\frac{\sqrt{3}}{2}\mu \text{F},R_2=20\text{k}\Omega ,L=\frac{\sqrt{3}}{10}\text{H}$ and $R_1=10\Omega$. Current in $L-R_1$ path is $I_1$ and in $C-R_2$ path is $I_2$. The voltage of $A.C.$ source is given by, $V=200\sqrt{2}\sin \left(100t\right)\text{V}$. The phase difference between $I_1$ and $I_2$ is:

1. ${30}^{\circ }$
2. ${60}^{\circ }$
3. $0^{\circ }$
4. ${90}^{\circ }$

Q. A capacitor of capacitance 1uF is charged to a potential of 1V. It is connected in parallel to an inductor of inductance 10^{-3}H. The maximum current that will flow in the circuit has the value 1) \sqrt{ (1000)} mA 2) 1mA 3) 1 uA 4) 1000 mA

Q. A parallel plate capacitor of capacitance C is charged to a potential V? It is then connected to another uncharged capacitor having the same capacitance? Find out the ratio of energy stored in the combined system to that stored initially in a single capacitance?

Q. In the given circuit, the $AC$ source has $\omega =100\text{rad/s}$. Considering the inductor and capacitor to be ideal, the correct choice(s) is (are):

1. The current through the source, $I$ is $0.3\text{A}$.
2. The current through the source, $I$ is $0.3\sqrt{2}\text{A}$.
3. The voltage across $100\Omega$ resistor is $10\sqrt{2}\text{V}$.
4. The voltage across $50\Omega$ resistor is $10\text{V}$

Q. A 400 $\Omega$ resistor, a 250 $mH$ inductor and a $2.5\mu F$ capacitor are connected in series with an $AC$ source of peak voltage 5 $V$ and angular frequency $2kHz$. What is the peak value of the electrostatic energy of the capacitor?

1. $2\mu J$
2. $2.5\mu J$
3. $3.33\mu J$
4. $5\mu J$

Q. A wire whose cross sectional area is increasing linearly from its one end to the other, is connected across a battery of V volts.which of the following quantities remain constant in the wire?(a)drift velocity(b)current density (c) electric current (d) electric field.justify your answer.

Q. In $LC$ circuit the inductance $L=40\text{mH}$ and capacitance $C=100\mu \text{F}.$ If a voltage $V\left(t\right)=10\sin \left(314t\right)$ is applied to the circuit, the current in the circuit is given as

1. $0.52\cos \left(314t\right)$
2. $10\cos \left(314t\right)$
3. $5.2\cos \left(314t\right)$
4. $0.52\sin \left(314t\right)$

Q. AC voltage, $V\left(t\right)=20\sin \left(\omega t\right)$, of frequency $50\text{Hz}$, is applied to a parallel plate capacitor. The separation between the plates is $2\text{mm}$ and the area of the plates is $1{\text{m}}^2$. The amplitude of the oscillating displacement current, for the applied AC voltage is -

Take ${ϵ}_0=8.85\times {10}^{-12}\text{F/m}$

1. $83.37\mu \text{A}$
2. $55.58\mu \text{A}$
3. $21.14\mu \text{A}$
4. $27.79\mu \text{A}$

Q. A capacitor $C=2\mu \text{F}$ and an inductor with $L=10\text{H}$ and coil resistance $5\Omega$ are in series in a circuit. When an alternating current of $rms$ value $2\text{A}$ flows in the circuit, the average power $\left(\text{in W}\right)$ in the circuit is

1. $100$
2. $50$
3. $20$
4. $10$

Q. A16 ohm resistance wire is bent to form a square. A source of 9 volt is connected across one of its sides calculate the potential difference across any one of its diagonal

Q. An inductance of 1 mH and a charged capacitor capacitance of 10$\mu$F are connected across each other. The resonating angular frequency of circuit is

1. ${10}^{5}rad/s$
2. ${10}^{4}rad/s$
3. ${10}^{3}rad/s$
4. ${10}^{2}rad/s$

Q. A battery of six cells each of e.m.f. 2 V and internal resistance 0.5 oh is being charged by D. C. mains of e.m.f.220 V by using an external resistance of 10 ohm What will be the charging current?

Q. Figure shows two capacitors connected in series and joined to a battery. The graph shows the variation in potential as one moves from left to right on the branch containing the capacitors.

1. $C_1>C_2$
   
2. $C_1=C_2$
   
3. $C_1<C_2$
   
4. The information is not sufficient to decide the relation between $C_1$ and $C_2$.

Q. A series combination of two capacities of value 0.1 microfarad and 1 microfarad is connected with a source of voltage 500 volts. The potential difference in volts across the capacitor of value 0.1 microfarad will be :
(1) 50
(2) 500
(3) 45.5
(4) 454.5

Q. There is a circuit diagram in which capacitors, resistors and battery are given. Then choose the correct option(s) (Assume initially all the capacitors are uncharged).

1. At steady state, charge on capacitor $A$ is zero
2. At steady state, charge on capacitor $B$ is zero
3. At steady state, charge on capacitor $B$ is $40\mu C$
4. Electric current in $2\Omega$ resistor is $5\text{A}$

Q.

A source of sound emitting a 1200 Hz note travels along a straight line at a speed of $170m{s}^{-1}$. A detector is placed at a distance of 200 m from the line of motion of the source. (a) Find the frequency of sound received by the detector at the instant when the source gets closest to it. (b) Find the distance between the source and the detector at the instant it detects the frequency 1200 Hz. Velocity of sound in air $=340m{s}^{-1}$.

Q. An inductor $(X_L=2\Omega )$ , a capacitor $(X_C=8\Omega )$ and a resistance $\left(8\Omega \right)$ are connected in series with an ac source. The voltage output of $A.C$ source is given by $v=10\cos 100\pi t$. The instantaneous potential difference between $A$ and $B$ is equal to $x\times {10}^{-1}volt$, when it is half of the voltage output from source at that instant. Find out value of $x$________

Q. 40.What should be the value of r so that no current flows throw 6 volt battery

Q. A parallel plate capacitor of capacity C has been charged so that the potential difference between its plates is V. Now the plates of this capacitor are connected to another uncharged capacitor of capacity 2C. The common potential acquired by system is

Q. 125.Find the potential diference across the capacitor in volts? 1)4V 2)2V 3)1V 4)8V .

Q. when a series combination of induc†an ce and resis†an ce are connected with a10v, 50Hz a.c source , a current of 1A flows in the circuitb.the voltage leads the current by a phase angle of π/3 radian . calculate the valuesvof resis†an ce and inductive reac†an ce .

Q. In a circuit consisting of a capacitance and a generator with alternating emf \(E_g=E_{g}\sin \omega t\), where \(V_C\) and \(I_C\) are the voltage and current. Correct phasor diagram for such circuit is :

Q. Two capacitors each having capacitance $2\mu \text{F}$ and breakdown voltage $1.5\text{V}$ are joined in series. The breakdown voltage of the combination will be

1. $1.5\text{V}$
2. $4.5\text{V}$
3. $7.5\text{V}$
4. $3.0\text{V}$

Q. The fundamental frequency of a string stretched with a weight of $4kg$ is $256Hz$. The weight required to produce its octave is -

1. $4kgwt$
2. $12kgwt$
3. $16kgwt$
4. $24kgwt$

Q. A charged capacitor is allowed to discharge through a resistance $2\Omega$ by closing the switch $S$ at the instant $t=0$. At time$t=\ln 2\mu \text{s}$, the reading of the ammeter falls half of its initial value. the resistance of the ammeter equals to

1. $0\Omega$
2. $2\Omega$
3. $\infty$
4. $2M\Omega$

Q. If an LC circuit has C= 1uF and L=0.25 henry, neglecting any resistance in the circuit, what is the frequency of oscillation?
(BHU 2003; MP PMT 2005)

1. 812Hz
2. 100Hz
3. 576Hz
4. 318Hz