A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring- mass damped oscillator having damping constant b, mass m and oscillating with a force constant k, the correct equivalence will be

Options

A. `L harr k, C harr b, R harr m`
B. `L harr m, C harr (1)/(k), R harr b`
C. `L harr (1)/(b), C harr (1)/(m), R harr (1)/(k)`
D. `L harr m, C harr k, R harr b`

Answer

B

Explanation

Equation of damped oscillations,
`-kx- bv- ma`
`:. ma + bv- kx = 0`
`:. m= (d^(2)x)/(dt^(2)) + (dx)/(dt) + kx = 0` …(1)

Now, for LCR circuit, according to Kirchoff.s second law,
`-L (dI)/(dt) - RI -(q)/(c )= 0`
`I= (dq)/(dt) " hence" (dI)/(dt) = (d^(2) q)/(dt^(2))`
`:. L (d^(2) q)/(dt^(2)) + R (dq)/(dt) + (q)/(a) = 0`...(2)
By comparing equation (1) and (2)
`L harr m, R harr b, (1)/(C ) harr k`