Obtain the relation of voltage applied to a series LCR circuit.

Explanation

Below figure shows a series LCR circuyit connected to an AC source `.epsilon.`. Voltage of an AC source is `V = V_(m) sin omega t `.

Let q is the charge on the capacitor and I the current at time t,
`:. V = V_(L ) + V_(R ) + V_( C )`
From Kirchhoff.s loop rule `L ( dI)/( dt) + IR + ( q )/( C ) = V `
From Kirchhoff.s loop rule `L (dI)/(dt) + IR + ( q)/( C ) = V ` where potential difference across the ends `= L (dI)/( dt )`
potential difference across the ends of capacitor `= ( q )/( C )` and potential difference across the ends of resistance `= I_(R )`.