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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))`
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