L-C Oscillatory Circuit (Board Level)

Video Lecture

Theory For Notes Making

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Objective Assignment

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Subjective Assignment

Q.1

Obtain an expression for the frequency of oscillations when a capacitor discharges itself through an inductor.

Q.2

In an LC Oscillatory circuit without resistance

(i) Find the equation of instantaneous charge on the capacitor

(ii) Find the equation of instantaneous current in the circuit

(iii)Prove that at any instant the total energy in the circuit is equal to the initial energy stored in the capacitor.

Q.3

A 10 mF capacitor is charged to a 25 volt of potential. The battery is then disconnected and pure 100 mH coil is connected across the capacitor so that LC oscillations are set up. Calculate max. current in the coil.

Ans. 0.25 A

Q.4

A charged 30 mF capacitor is connected to a 27 mH inductor. What is the angular frequency of free oscillations of the circuit?

Ans. 1.1´10³ rad/s

Q.5

find the natural frequency of a circuit containing inductance of 100 mH and a capacity of 0.01 mF. To which wavelength, its response will be maximum? For how long will the oscillations continue?

Ans. 159.2 kHz, 1.884´10³ m, ¥

Q.6

A 20 mF capacitor is charged to 30 V potential. The battery is then disconnected and a 200 mH coil is connected across it so that LC oscillations are set up. Calculate the frequency of the oscillations set up and the maximum current in the coil.

Ans. 79.6 hz, 0.3 A

Q.7

A 1.5 mF capacitor is charged to 57 volt. The charging battery is then disconnected and a 12 mH coil is connected across the capacitor so that LC oscillations occur. If resistance in the circuit is zero, what is the maximum value of current in the coil?

Ans. 637.2 mA

Q.8

A coil of 10mH is connected to a charged capacitor of 25 micro farad with an initial charge of 20mC. At t=0 the circuit is closed. If T is the time period of oscillation of charges in the circuit, then find

(i) Time period of oscillations T

(ii)Maximum energy in the circuit

(iii) Time instants at which all the energy of the circuit is electrical

(iv) Time instants at which all the energy of the circuit is magnetic

(v) ) Time instants at which the energy of the circuit is half electrical and half magnetic

(vi) Current in the circuit when the charge on the capacitor is half of its maximum value.

(vii) If a resistance of 1000 ohm is inserted in the circuit ,how much energy will eventually be dissipated as heat.

QUIZ

Created on August 10, 2022 By

physicscart

L-C Oscillatory Circuit (Basic Level)

1 / 10

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

600 radian

600 Hz

500 radian

500 Hz

2 / 10

In LCR circuit, the capacitance is changed from C to 4C. For the same resonant frequency, the inductance should be changed from L to

L / 2

L / 4

3 / 10

In general in an alternating current circuit

The average value of current is zero

The average value of square of the current is zero

Average power dissipation is zero

The phase difference between voltage and current is zero

4 / 10

The root mean square value of the alternating current is equal to

Twice the peak value

Half the peak value

\frac{1}{{\sqrt{2}}}

times the peak value

Equal to the peak value

5 / 10

A generator produces a voltage that is given by $V=240\sin 120\,t$ , where t is in seconds. The frequency and r.m.s. voltage are

60 Hz and 240 V

19 Hz and 170 V

754 Hz and 70 V

None of These

6 / 10

The r.m.s. value of an ac of 50 Hz is 10 amp. The time taken by the alternating current in reaching from zero to maximum value and the peak value of current will be

2 x 10–2 sec and 14.14 amp

1 x 10–2 sec and 7.07 amp

5 x 10–3 sec and 7.07 amp

5 x 10–3 sec and 14.14 amp

7 / 10

The frequency of ac mains in India is

30 c/s or Hz

50 c/s or Hz

60 c/s or Hz

120 c/s or Hz

8 / 10

The potential difference V and the current i flowing through an instrument in an ac circuit of frequency f are given by $V=5\cos \omega \,t$ volts and I = 2 sin wt amperes (where w = 2 $\displaystyle \pi$ f). The power dissipated in the instrument is

10 W

5 W

2.5 W

9 / 10

The natural frequency of a L-C circuit is equal to

\frac{1}{{2\pi }}\sqrt{{LC}}

\frac{1}{{2\pi \sqrt{{LC}}}}

\frac{1}{{2\pi }}\sqrt{{\frac{L}{C}}}

\frac{1}{{2\pi }}\sqrt{{\frac{C}{L}}}

10 / 10

If ${{E}_{0}}$ represents the peak value of the voltage in an ac circuit, the r.m.s. value of the voltage will be

\frac{{{{E}_{0}}}}{\pi }

\frac{{{{E}_{0}}}}{2}

\frac{{{{E}_{0}}}}{{\sqrt{\pi }}}

\frac{{{{E}_{0}}}}{{\sqrt{2}}}

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L-C Oscillatory Circuit (Board Level)

Theory For Notes Making

Objective Assignment

Subjective Assignment

On Line Test

Video Lecture

Theory For Notes Making

Objective Assignment

Subjective Assignment

QUIZ