Home
Class 12
PHYSICS
A LCR circuit behaves like a damped harm...

A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring mass damped oscillator having damping constant ‘b’. If the amount of initial charge on the capacitor be `Q_(0).` then the amplitude of the amount of charge on the capacitor as a function of time t will be:

A

`Q = Q_(0)e ^(-(Rt)/(2I))`

B

`Q = Q_(0)(1-e ^((2Rt)/(L )))`

C

`Q = Q_(0)e ^(-(Rt)/(L ))`

D

`Q = Q _(0)(1-e ^(-(Rt)/(L )))`

Text Solution

Verified by Experts

The correct Answer is:
A
For damped oscillatin: `ma + bv + kx=0`
`m (d ^(2) x )/(dt ^(2)) + b (dx )/(dt) + kx =0" "…(i)`
For LCR series circuit:
`-iR-L (di)/(dt) - q/C =0`
`L (d ^(2) q )/(dt ^(2)) + R (dq )/(dt) + 1/C q =0" "(ii)`
Comparing (i) & (ii), L `to 1/k, R to b`
Amplitude `A = A _(0)e ^((bt)/(2m))" "therefore` Amplitde charge `Q = Q_(0)e^((Rt)/(2L))`
Doubtnut Promotions Banner Mobile Dark
|

Similar Questions

Explore conceptually related problems

Initially the capacitor is uncharged find the charge on capacitor as a function of time, if switch is closed at t=0.

For a damped oscillator damping constant is 20gm/s, mass is 500gm. Find time taken for the amplitude to become half the initial

Knowledge Check

  • An LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring mass damped oscillator having damping constant b, the correct equivalence of b would be:

    A
    `b harr R`
    B
    `b harr c`
    C
    `b harr (1)/(R )`
    D
    `b harr (1)/(L)`

  • An LCR series circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant ‘b’, the correct equivalence would be (Take, i = current, V = voltage, x = displacement, q = charge, F = force, v = velocity)

    A
    `qharrx,vltharrgti,FharrV`
    B
    `qharrv,iharrx,FharrV`
    C
    `qharrx,vharrV,Ftoi`
    D
    `qharrF,iharrx,Vtov`

  • A LCR circuit be haves like a damped harmonic oscillator. The discharge of capacitor C, through an C^(square) inductor L having resistance R is oscillatory. Then which of following is correct _____.

    A
    `(1)/(LC) lt (R^(2))/(4L^(2))`
    B
    `(1)/(LC) gt (R^(2))/(4L^(2))`
    C
    `(1)/(LC) gt (R^(3))/(4L^(4))`
    D
    `(1)/(sqrt(LC)) gt (R^(3))/(8)`

    • Similar Questions

    Explore conceptually related problems

    A capacitor of capacitance C is given a charge Q. At t=0 ,it is connected to an uncharged of equal capacitance through a resistance R. Find the charge on the second capacitor as a function of time.

    In an oscillating LC circuit, L = 25.0 mH and C = 2.89 muF . At time t=0 the current is 9.20 mA, the charge on the capacitor is 3.80 muC and the capacitor is charging. What are (a) the total energy in the circuit, (b) the maximum charge on the capacitor, and (c) the maximum current? (d) If the charge on the capacitor is given by q= cos (omega t+ phi) , what is the phase angle phi ? (e) Suppose the data are the same, except that the capacitor is discharging at t= 0. What then is phi ?

    A circuit with capacitance C and inductance L generates free damped oscillations with current varying with time as I=I_(m)e^(-betat) sin omegat . Find the voltage across the capacitor as a function of time, and in particular, at the moment t=0 .

    Time constant of a C-R circuit is 2/(ln(2)) second. Capacitor is discharged at time t=0 . The ratio of charge on the capacitor at time t=2s and t=6s is

    If initial amplitude during a damped oscillation of mass m is 12 cm and after 2s it reduces to 6cm then find damping constant(b)

    Home
    Profile