Question

- 10 uF For the circuit shown, Vs (t) = 200 sin (itt/2) V. (a) Find and plot the energy stored, and the power dissipated in the capacitance as functions of time showing the period (T) and maximum value of each. (b) Calculate the energy dissipated in the resistance for one complete cycle. 102 S2

Answer 1

Consider the o given circuit: vs joke I LOVE Voltage Vc (t) across scure voltage. the capacitor is same as Vc (t) = Vs 4) Vect) = 400 sin () v Therefore ca) = c dui * ** ** et feru stiu ()} A = 10.2 x 200 x x Cos (+) A 3 314 x 10-5 cos(Tt) A

miellt) = 3.14 Cos (*) ma Therefore, Power dissipated in the Capacitor is: Polt) = V, 1) x176) = Loo sin ( ) * 3.14 cos () mw = 698 sin (+) C (1) mw = 0.38 * fa cinque) 6 CE)} w = 0.314 x sin (ft x 2) W + Pilt = 0.314 x sin (Tt) W The period of the source voltage signal is: Toe ons T = 48

Capacity as a function - Energy stored in the of time is given as: Ec = P, (t) at son cifre), de op [- carnet) of Care) - ww] : -0.314 Cos (tt) - : - 0 F C Got) - ' ] = 0.314 (- Coret) Ec = 100 (-Cos Tt) ms

Therefore, the graph of Energy is as follow: 2001- (MJ) a ' 27 't And the plot of power is as follow: Pelt) = 0.314 sú (Tt) W Pelt) 2/ 3 3 - 2

(6) current let) in the Resistance is: ir (t) = Ush) ma lo = so sin (14) mA = IR W) = 20 sin(Tt) ma * Power , PRt is: PR (t) = VCH) xialt) = 400 sin!(!) mw Pect) 4 sin() w - Energy dissipated for one cycle is: so sranya :/ *(*) as

= 4 elt naf 1 color) ef (r-Gerav = ? Cow?- df [sin nt). = 8(4-0) - (sin (409 - sincer] 8 - (0-0) Energy stooed in one complete cycle is 8J.