LC Oscillation

Q. A coil of inductance $300\text{mH}$ and resistance $2$ $\Omega$ is connected to a source of voltage $2\text{V}$. The current reaches half of its steady state value in

Take $\ln 2=0.693$

1. $0.15\text{s}$
2. $0.3\text{s}$
3. $0.05\text{s}$
4. $0.1\text{s}$

Q. A solenoid of inductance $50\text{mH}$ and resistance $10\Omega$ is connected to a battery of $6\text{V}.$ The time elapsed before the current acquires half of its steady state value from zero is-
$(\ln 2=0.693)$

1. $10\text{ms}$
2. $3.5\text{ms}$
3. $0.25\text{ms}$
4. $7\text{ms}$

Q. The frequency of oscillation of current in the inductor is

1. $\frac{1}{6\pi \sqrt{LC}}$
2. $\frac{1}{\sqrt{LC}}$
3. $\frac{1}{3\sqrt{LC}}$
4. $\frac{1}{2\pi \sqrt{LC}}$

Q. In an a.c circuit, the resistance $R=0.2\Omega$. At a certain instant $V_A-V_B=0.5\text{V},i=0.5\text{A}$ and the current $i$ is increasing at the rate of $\frac{\Delta i}{\Delta t}=8{\text{As}}^{-1}$. The inductance of the coil is

1. $0.02\text{H}$
2. $0.01\text{H}$
3. $0.5\text{H}$
4. $0.05\text{H}$

Q. An emf of $20\text{V}$ is applied at time $t=0$ to a circuit containing in series $10\text{mH}$ inductor and $5\Omega$ resistor. The ratio of the current at time $t=\infty$ and $t=40\text{s}$ is close to:
(Take $e^2=7.389$)

1. $1.06$
2. $1.15$
3. $1.46$
4. $0.84$

Q. In the circuit shown, the value of current I in Ampere is (Write upto two digits after the decimal point)

Q. In the steady state condition, the rate of heat produced in a choke coil is $P$. The time constant of the choke coil is $\tau$. If now the choke coil is short circuited, then the total heat dissipated in the coil is :

1. $P\tau$
2. $\frac{1}{2}P\tau$
3. $\frac{P\tau }{\ln \left(2\right)}$
4. $P\tau \ln \left(2\right)$

Q. A $44mH$ inductor is connected to $220V$, $50Hz$ ac supply. The RMS value of the current in the circuit is

1. 12.8 A
2. 13.6 A
3. 15.9 A
4. 19.5 A

Q. Two different coils have self inductance $8mH$ and $2mH$. The current in both coils are increased at same constant rate. The ratio of the induced emf's in the coil is :

1. $4:1$
2. $1:4$
3. $1:2$
4. $2:1$

Q. The natural frequency of an LC - circuit is $1,25,000$ cycles per second. Then the capacitor C is replaced by another capacitor with a dielectric medium of dielectric constant k. In this case, the frequency decreases by $25kHz$. The value of k is:

1. $3.0$
2. $2.1$
3. $1.56$
4. $1.7$

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

1. $2W$
2. $1W$
3. $4W$
4. $16W$

Q. A coil of inductance $8.4\text{mH}$ and resistance $6\Omega$ is connected to a $12\text{V}$ battery. The current in the coil is $1\text{A}$ at approximately the time is-

1. $5\text{s}$
2. $2\text{ms}$
3. $10\text{s}$
4. $1\text{ms}$

Q. The rms voltage of domestic electricity supply is $220$ volt. Electrical appliances should be designed to withstand maximum instantaneous voltage of

1. $310V$
2. $220V$
3. $440V$
4. $330V$

Q. Two resistances are expressed as $R_1(4\pm$ 0.5 %)$\Omega$ and $R_2(12\pm$ 0.5 %)$\Omega$. The net resistance when they are connected in series with percentage error is:

1. $(16\pm$ 0.5 %) $\Omega$
2. $(16\pm$ 6.25 %) $\Omega$
3. $(16\pm$ 22 %) $\Omega$
4. $(16\pm$ 2.2 %) $\Omega$

Q. The rms value of current in an ac circuit is $10A$. What is the peak current?

Q. A coil of inductance 200 H and resistance $20\Omega$ is connected to a constant voltage source. How soon in seconds will the coil current reach 50% of the steady state value?(ln2 = 0.693). Write upto two digits after the decimal point.

Q. Two coils have self-inductance $L_1=4$$mH$ and $L_2=1$$mH$ respectively. The currents in the two coils are increased at the same rate. At a certain instant of time both coils are given the same power. If $i_1$ and $i_2$ are the currents in the two coils, at that instant of time respectively, then the value of ($i_1$ /$i_2$ ) is :

1. $\frac{1}{8}$
2. $\frac{1}{4}$
   
3. $\frac{1}{2}$
4. $1$

Q. The frequency of oscillation of current in the inductor is

1. $\frac{1}{3\sqrt{LC}}$
2. $\frac{1}{6\pi \sqrt{LC}}$
3. $\frac{1}{\sqrt{LC}}$
4. $\frac{1}{2\pi \sqrt{LC}}$

Q. Each resistance of given figure is of $10\Omega .$ Then current I through cell of 40 V isA. [Write upto 2 digits after the decimal.]

Q. A coil of self inductance $2\cdot 5H$ and resistance $20\Omega$ is connected to a battery of emf 120V having internal resistance of $5\Omega$. Find the time constant of the circuit.

Q. A coil of $n$ turns and radius $r$ is placed in a magnetic field. The electrical power is dissipated due to the current induced in the coil. By stretching the wire, if the number of turns were to be quadrupled and the wire radius halved, the electrical power dissipated would be :

1. halved
2. the same
3. doubled
4. quadrupled

Q. When the current changes from $+2A$ to $-2A$ in $0.05$ second, an e.m.f. of $8V$ is induced in a coil. The coefficient of self-induction of the coil is :

1. $0.4H$
2. $0.8H$
3. $0.2H$
4. $0.1H$

Q. Two series resistors are connected to an ac source. If there are $7.5V$ rms across one resistor and $4.2V$ rms across the other, the peak source voltage is

1. $16.54V$
   
2. $1.65V$
   
3. $10.60V$
   
4. $5.93V$
   

Q. When a current of 2 A is passed through a coil of 100 turns, flux associated with it is $5\times {10}^{-5}$ Wb.
Find the self inductance of the coil.

1. $4\times {10}^{-2}H$
2. $4\times {10}^{-3}H$
3. $2.5\times {10}^{-3}H$
4. ${10}^{-3}H$

Q. An emf induced in a secondary coil is $10000V$ when the current breaks in the primary. The mutual inductance is $5H$ and the current reaches to zero in ${10}^{-4}$ s in primary. The maximum current in the primary before the break is

1. $0.2A$
2. $0.4A$
3. $0.3A$
4. $0.5A$

Q. Two coils are at fixed locations. When coil 1 has no current and the current in coil 2 increases at the rate of $15.0A{s}^{-1}$, the emf in coil 1 is $25mV$. When coil 2 has no current and coil 1 has a current of $3.6A$, the flux linkage in coil 2 is

1. $16mWb$
2. $10mWb$
3. $4.00mWb$
4. $6.00mWb$

Q. A resonance circuit having inductance and resistance $2\times {10}^{-4}\text{H}$ and $6.28\Omega$ respectively oscillates at $10\text{MHz}$ frequency. The value of quantity factor of this resonator is_______

Q. In the circuit diagram shown $X_C=100\Omega ,X_L=200\Omega$ and $R=100\Omega .$ The effective through the source is:

1. $2A$
2. $\sqrt{2}A$
3. $4A$
4. $2\sqrt{2}A$

Q. The self induced emf of a coil is 25 volts. When the current in it is changed at uniform rate from 10 A to 25 A is 1 s, the change in the energy of the inductance is :

1. 540 J
2. 437.5 J
3. 637.5 J
4. 740 J

Q. A resonance circuit having inductance and resistance $2\times {10}^{-4}\text{H}$ and $6.28\Omega$ respectively oscillates at $10\text{MHz}$ frequency. The value of quantity factor of this resonator is_______