7.6 AC V OLTAGE A PPLIED TO A S ERIES LCR C IRCUIT

. AC V OLTAGE A PPLIED TO A S ERIES LCR C IRCUIT Figure . shows a series LCR circuit connected to an ac source ε . As usual, we take the voltage of the source to be v = v m sin ω t . If q is the charge on the capacitor and i the current, at time t , we have, from Kirchhoff’s loop rule: i L i R v ( . ) We want to determine the instantaneous current i and its phase relationship to the applied alternating voltage v . We shall solve this problem by two methods. First, we use the technique of phasors and in the second method, we solve Eq. ( . ) analytically to obtain the time– dependence of i . FIGURE . A series LCR circuit connected to an ac source.