Question

10-13 please

For the damping circut nown below, assume the Cactor has an initial voltage > O volts LICI 10 Calculate the value of Rl to cause the damping of the volta At node 1 with respect to node 0 ) to be critically damned 11 In a series RLC Circuit, setting R=0 will produce a overdamping c. underdamping Answer: b no damping d. critical damping (letter) #12 For the circuit shown below, the switch has been open for a long time. What is the voltage across the capacitor just before the switch is closed (t=0) t= 0 problems 13 & 14 Answer: a 2V b. 12V c.0V d. 4V (letter) #13 Find the current through RI after the switch has been closed for a long time ( time à infinity ). a 31.25 mV c. 5.0 mV Answer: b. O d 20 my (letter)

Answer 1

+ 2 XV LF23 VT G=lom F hott cdu=0 Vorovsto Apply KCL at top node Vt stue R LJ . at Taking derivative wrot to time cd²vt ldv + v =0 at Ridt L d²v tl du + Lv=o. at² RC at LC Taking Laplace transfom (52 7 Best Ic) vls) = 0 Characteristic equation S2 + I Std So . RC LC npared with 52 + 2zw. Stw.2= 0 weten te 2x10x103 camere jou = 50 W = 150 = 7.071 radds

for critical damping damping Hatie_2=1 States 1 30 52+ 23 un SF 103 = 0 BC 217.071) = jooo R. (10) - Ri= 1000 2171671) (10) 7607152 - O In Series Ric cirwit Characterstic equation is - $2+ksuto compare with LC 5 2+236. St49220 27w, = ſme - R=0 damping natio 3 = 0 means system is Undamped (no damping) @_no damping After very long time. At too Capacitor act as oben cir wit & inductor act as short cirwit.

At tto- - R=22 ilot RITR2 Hoy = 12. 2A Apply KVL around look 12-1R - V. (0)=0 12-2(4) = V(10) - Vele) = 12-8= 4 V - Vele) = VE 10) = Velot) = Y V option € - Attro -R=454 12V HAt-steady state inductor t& capacitor exchange energy & become act as an At Steady state tisas I=o thueough Rt I open urwit REur IEO 19V foption or