(a) The equation for the current i in the LCR circuit can be written as
where the charge q on the capacitor is given by
We consider a steady-state solution of Eqn. (4.44) in the form (after the alternating emf has been applied for some time)
Substituting Eqn. (4.46) into Eqn. (4.44) and equating the coefficients of sin ωt and cos ωt from both sides, we get
(b) From Eqn. (4.49), we find that the maximum value of I occurs when
(c) The value of I at resonance is I0 = E0/R and the phase angle φ is zero at resonance.