question_answer 55)

  For an LCR circuit driven at frequency , the equation reads (i) Multiply the equation by  and simplify where possible. (ii) Interpret each term physically. (iii) Cast the equation in the form of a conservation of energy statement. (iv) Intergrate the equation over one cycle to find that the phase difference between  and  must be acute.

Answer:

                  For an LCR circuit driven at frequency , the given eqn. is                     ??(i) Multiplying both sides by , we get                ??.(ii) Now, = rate of change of energy stored in inductor = rate of Joule heating loss = rate of change of energy stored in capacitor  = rate at which driving force pours in energy Hence, eqn. (ii) is in the form of conservation of energy statement. Integrating both sides of (ii) w.r.t.  over one full cyclewe may write  , which is possible only when phase diff. between  andis an acute angle.