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Compare LC oscillations and a force damp...

Compare LC oscillations and a force damped oscillations in mechanics.

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The equation of forced damped oscillations is,
`(d^(2)x)/( dt^(2)) + ( b)/( m ) ( dx)/( dx) + ( k )/( m ) x = (F_(0) )/( m) cos omegat` and equation of LC oscillation,
`(d^(2)q)/( dt^(2))+( R )/( L ) (dq)/( dt) + = ( V_(m))/( L ) sin omega t `
`{:("Forced oscillations","Driven LCR circuit"),(m(d^(2)x)/(dt^(2))+b(dx)/(dt) kx = F cos omega_(d)t,L(d^(2)q)/(dt^(2)) + R (dq)/( dt) + (q)/(C ) = V_(m) sin omega t ),("Displacement x ","Charge on capacitor q"),("Time t","Time t"),("Mass m","Self inductance L"),("Damping constant b","Resistance R"),("Spring constant K","Inverse capacitance "1//C),("Driving frequency" omega_(d),"Driving frequency " omega),("Natural frequency of oscillations"omega,"Natural frequency of LCR circuit " omega_(0)),("Amplitude of forced oscillations A","Maximum charge stored "q_(m)),("Amplitude of driving force "F_(0),"Amplitude of applied voltage"v_(m)):}`
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KUMAR PRAKASHAN-ALTERNATING CURRENTS -SECTION-A (QUESTIONS-ANSWERS)
  1. Obtain an equation for sharpness of resonance in an L-C-R series AC ci...

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  2. Obtain the equation of the bandwidth for an L-C-R series AC circuit an...

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  3. What is sharpness of resonance ? Derive equation of Q-factor

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  4. If L= 1.00 mH, C = 1.00nF, then find the resonant frequency.

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  5. Define the power for AC circuit. Obtain an equation of average power f...

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  6. Write an equation of average power for L-C-R series AC circuit and dis...

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  7. What is meant by LC circuit? What are LC oscillations ?

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  8. Obtain the differential equation for a LC circuit.

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  9. Solve the differential equation of L-C circuit and obtain the expressi...

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  10. Explain how LC oscillations takes place in the circuit.

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  11. Compare the oscillations in an LC circuit are analogous to the oscilla...

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  12. For which 2 reasons the discussion of LC oscillations is not realistic...

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  13. Compare LC oscillations and a force damped oscillations in mechanics.

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  14. What is transformer ? Write its principle and write its construction.

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  15. Write the working procedure of transformer.

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  16. Using the equation of power for an ideal transformer, prove (I(p))/( I...

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  17. How a transformer affects the voltage and current ?

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  18. Due to which reasons the energy losses do occurs in actual transformer...

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  19. Explain the use of transformer for distribution of power over long dis...

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  20. Write important uses of transformer.

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