Electrical Oscillations

Q. A series LCR circuit with inductance $10H$, capacitance $10\mu F$, resistance $50\Omega$ is connected to an ac source of voltage, $V=200\sin \left(100t\right)$ volt. If the resonant frequency of the LCR circuit is $v_0$ and the frequency of the ac source is $v$, then

Q. A capacitor of capacitance $2\mu F$ is charged to $40V$ and another capacitor of capacitance $4\mu F$ is charged to $20V$. If the capacitors are connected together in same polarity, then the energy lost in reorganisation of charge will be

1. $316.2\mu J$
2. $266.67\mu J$
3. $402\mu J$
4. $191.6\mu J$

Q.

In an oscillating LC circuit, the maximum charge on the capacitor is $Q$. The charge on the capacitor, when the energy is stored equally between the electric and magnetic field is:

Q.

In a series LCR resonant circuit, the quality factor is measured as $100$. If the inductance is increased by two fold and resistance is decreased by two fold, then the quality factor after this change will be __________. (up to two decimal places).

Q.

Assertion: Faradays laws are consequences of the conservation of energy.

Reason: In a purely resistive A.C. circuit, the current lags behind the e.m.f.

1. Both A and R are true and R is the correct explanation of A

2. Both A and R are true but R is not the correct explanation of A

3. A is true but R is false

4. A and R are false

Q. The charge on the 6uF capacitor in the circuit shown is?

Q.

A current of $2A$is increasing at a rate of $4A/s$ through a coil of inductance$2H$. What is the energy stored in the inductor per unit of time?

Q. 12.Draw a circuit diagram showing a dry cell connected to a bulb through a switch.Mark the positive and the negative terminals of the cell, and the direction of flow of a.electron, b.conventional current

Q. In free space, a particle $A$ of charge $1\mu \text{C}$ is held fixed at a point $P$. Another particle $B$ of the same charge and mass $4\mu \text{g}$ is kept at a distance of $1\text{mm}$ from $P$. If $B$ is released, then its velcoity at a diatnce of $9\text{mm from}P$ is
$[\text{Take}\frac{1}{4\pi {\epsilon }_0}=9\times {10}^9{\text{Nm}}^2{\text{C}}^{-2}]$

1. $2.0\times {10}^3\text{m/s}$
2. $3.0\times {10}^4\text{m/s}$
3. $1.5\times {10}^2\text{m/s}$
4. $1.0\text{m/s}$

Q.

A bulb and a capacitor are connected in series to a source of alternating current. If its frequency is increased, while keeping the voltage of the source constant, then

Q. An LC resonant circuit contains a $400pF$ capacitor and a $100\mu H$ inductor. It is set into oscillation coupled to an antenna. The wavelength of the radiated electromagnetic waves is

1. 377.14 $mm$
2. 377.14 $m$
3. 377.14 $cm$
4. 3.7714 $cm$

Q. In the circuit shown in the figure, time constant and steady state current will be

1. $0.25\text{s},0.25\text{A}$
2. $0.75\text{s},0.75\text{A}$
3. $0.25\text{s},0.75\text{A}$
4. $0.5\text{s},0.75\text{A}$

Q. An inductance of 1 mH a condenser of $10\mu F$ and a resistance of $50\omega$ are connected in series. The reactance of inductor and condensers are same. The reactance of either of them will be

1. $30\omega$
2. $3.2\omega$
3. $10\omega$
4. $100\omega$

Q. A device 'X' is connected to an ac source $V=V_{0}sin\omega t$. The variation of voltage, current and power in one cycle is shown in the following graph:

(a) Identify the device 'X'.
(b) Which of the curves A, B and C represent the voltage, current and the power consumed in the circuit ? Justify your answer.
(c) How does its impedance vary with frequency of the ac source ? Show graphically.
(d) Obtain an expression for the current in the circuit and its phase relation with ac voltage.

Q.

A charged particle oscillates about its mean equilibrium position with a frequency of ${10}^{9}Hz$. The frequency of the electromagnetic wave produced by the oscillator is

1. $10Hz$

2. ${10}^{5}Hz$

3. ${10}^{9}Hz$

4. ${10}^{10}Hz$

Q. (a) For a given AC, $i=i_{m}sin\omega t$, show that the average power dissipated in a resistor $R$ over a complete cycle is $\frac{1}{2}{i}_m^{2}R$.
(b) A light bulb is rated at $100W$ for a $220V$ AC supply. Calculate the resistance of the bulb.

Q. Average heat produced per unit time during a cycle of $AC$ is the same as produced by $DC$ with current $i=$

1. $i_{avg}$
2. $i_{rms}$
3. $i_{avg}^2$
4. $i_{peak}$

Q.

Acceptor circuit is?

Q. A coil of self inductance $10\text{mH}$ and resistance $0.1\Omega$ is connected through a switch to a battery of internal resistance $0.9\Omega$. After the switch is closed, the time taken for the current to attain $80\%$ of the saturation value is
$[\text{take}\ln 5=1.6]$

1. $0.002\text{s}$
2. $0.103\text{s}$
3. $0.324\text{s}$
4. $0.016\text{s}$

Q. The energy stored in the magnetic field if current of $5\text{A}$ produces a magnetic flux of $2\times {10}^{-3}\text{Wb}$ through a coil of $500$ turns is

​​​​​​​$[$1 Mark$]$

1. $2.5\text{J}$
2. $0.25\text{J}$
3. $250\text{J}$
4. $1.5\text{J}$

Q. A $2\mu F$ capacitor is initially charged to $20$ Volts and then shorted across a $8\mu H$ inductor. The maximum value of the current in the circuit (in $\text{A}$) is

Q. A coil has an inductance of $\frac{2.2}{\pi }H$ and is joined in series with a resistance of $220\Omega$. When an alternating emf of 220 V at 50 c.p.s is applied to it, then the wattless component of the rms current in the circuit is ?

1. $0.5A$
2. $0.7A$
3. $5A$
4. $7A$

Q. In the adjoining figure the impedance of the circuit will be

1. 120 ohm
2. 50 ohm
3. 60 ohm
4. 45 ohm

Q. For the arrangement shown in the figure. Find the frequency of oscillation.

1. $5\text{Hz}$
2. $3.9\text{Hz}$
3. $3\text{Hz}$
4. $1.9\text{Hz}$

Q.

In the series $LCR$ circuit at resonance, the applied ac voltage is $220V$. The potential drop across the inductance is $110V$. What is the potential drop across the resistance?

Q. Two inductors having self inductances, $2\text{mH}$ and $8\text{mH}$ are arranged such that the mutual inductance is $2\text{mH}$. Find the coupling constant.

1. $\frac{1}{3}$
2. $\frac{1}{4}$
3. $\frac{1}{2}$
4. $\frac{1}{5}$

Q. A parallel plate capacitor is connected to a battery. A metal sheet of negligible thickness is placed between the plates. If the sheet remains parallel to the plates of the capacitor then which one of the following statements is correct:

1. The battery will supply more charge
2. The capacitance will increase
3. The potential difference between the plates will increase
4. Equal and opposite charges will appear on the faces of the metal plate.

Q. Give equation to caoculate voltage across inductor, capacitor and resistor in series LCR circuit

Q. 78.A battery of emf 10 is connected to resistances as shown in fig. The pd bw the points A and B

Q. The current flowing through an ac circuit is given by $i=5\sin \left(120\pi t\right)A$
How long will the current take to reach the peak value starting from zero?