The terminals of a generator producing a voltage V are connected through a wire of resistance R and a coil of inductance L (and negligible resistance). A capacitor of capacitance C is connected in parallel with the resistance R, as shown in Figure 11.20. Show that the current i flowing through the resistance R is given by

Suppose that

(i) V = 0 for t

(ii) L = 2R²C

(iii) CR = 1/2n

and show that the equation reduces to

Hence, assuming that i = 0 and di/dt = 0 when t = 0, use Laplace transforms to obtain an expression for i in terms of t.

Transcribed Image Text:

di LCR- + L + Ri= V dt di dt