Question

For an LCR circuit driven at frequency ω, the equation reads

L di/dt+Ri+q/C=v_i=v_m sinωt

(i) Multiply the equation by i 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 v and i must be acute.

Answer 1

= rate of change of energy stored in an inductor.

Ri² = joule heating loss

q/C i = d/dt(q²/2C)=rate of change of energy stored in the capacitor.

vi = rate at which driving force pours in energy. It goes into (i) ohmic loss and (ii) increase of stored energy.

if phase difference, a constant is acute.