p33_069.pdf

69. (a) The energy stored in the capacitor is given by U E = q 2 / 2 C .Since q is a periodic function of t with

period T ,somustbe U E . Consequently, U E will not be changed over one complete cycle. Actually,

U E has period T/ 2, which does not alter our conclusion.

(b) Similarly, the energy stored in the inductor is U B = 2 i 2 L .Since i is a periodic function of t with

period T ,somustbe U B .

P avg T =( I rms E rms cos φ ) T = 1

2 T

E m I cos φ

where we substitute I rms = I/ √ 2and

E rms =

E m / √ 2.

(d) The energy dissipated by the resistor is

P avg , resistor T =( I rms V R ) T = I rms ( I rms R ) T = 1

2 T I 2 R.

(e) Since

E m I cos φ =

E m I ( V R /

E m )=

E m I ( IR/

E m )= I 2 R , the two quantities are indeed the same.