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An LCR series circuit behaves like a dam...

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

`q harr x, v harr i, F harr V `

B

`q harr v, i harr x , F harr V `

C

`q harr x, v harr V, F harr i `

D

`q harr F, i harr x , V harr v `

Text Solution

Verified by Experts

The correct Answer is:
A
For physical spring-mass damped oscillator :
`ma + bv + kx = 0`
`implies m (d^2x)/(dt^2) + b(dx)/(dt) + kx = 0 " " …(i)`
For LCR series circuit :
`- iR - L (di)/(dt) - q/c = 0`
`implies (Ld^2 q)/(dt) + R (dq)/(dt) + q/c = 0 " " ….(ii) `
Comparing eqn. (i) & (ii)
`x harr q, (dq)/(dt) harr (dx)/(dt) , q/c har kx " or " x harr q, i harr v, V harr F`.
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