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Mechanical Properties Of Fluids

Question
CBSEENPH11020789
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A transistor-oscillator using a resonant circuit with an inductor L (of negligible resistance) and a capacitor C in series produce oscillations of frequency f. If L is doubled and C is changed to 4C, the frequency will be

  • f/4

  • 8f

  • straight f divided by 2 square root of 2

  • f/2

Solution

C.

straight f divided by 2 square root of 2

In a series LC circuit, frequency of LC oscillations is given by
                        straight f space equals fraction numerator 1 over denominator 2 straight pi square root of LC end fraction
or           straight f proportional to fraction numerator 1 over denominator square root of LC end fraction
rightwards double arrow space space space space space straight f subscript 1 over straight f subscript 2 space equals space square root of fraction numerator straight L subscript 2 straight C subscript 2 over denominator straight L subscript 1 straight C subscript 1 end fraction end root
  Given comma space space space straight L subscript 1 space equals space straight L comma space space straight C subscript 1 equals straight C comma space space straight L subscript 2 space equals space 2 straight L comma space space straight C subscript 2 space equals space 4 straight C comma space space straight f subscript 1 space equals space straight f therefore space space space space space straight f over straight f subscript 2 space equals space square root of fraction numerator 2 straight L space cross times space 4 straight C over denominator LC end fraction end root space equals space square root of 8 rightwards double arrow space space space space space space space straight f subscript 2 space equals space fraction numerator straight f over denominator 2 square root of 2 end fraction

Some More Questions From Mechanical Properties of Fluids Chapter

What is periodic motion?

Write down the expression for the instantaneous velocity and acceleration of particle vibrating in simple harmonic motion.

How do you define the mean position of particle executing simple harmonic motion?

Define amplitude.

What is the net displacement of the particle executing simple harmonic motion in one complete oscillation?

Are all the periodic motions simple harmonic?

Does the time period of particle vibrating in simple harmonic motion depend upon its displacement?

Where will the particle executing simple harmonic motion have acceleration maximum and speed zero?

What is the average velocity of the particle executing simple harmonic motion over one complete oscillation?

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