Question

Tylors Series
Solve by using the second Order Taylors Series Method. Assume step size h=0.3 Consider the RC circuit which is shown in the figure below. The charge Q across the capacitor at time to sec is o Coulomb, which is Q(0)=0 Coulomb, Given that C=2 F, R=12, and Vpc =5 V. The switch is closed at time t=0 sec, and the differential equation concerning the circuit is given as 99-1 -Q+ CV ).where Q is the charge stored in the capacitor and it is a function of time tin seconds VOC

Answer 1

to for to the switch was opened. The circuit becomes. uut There is no supply connected to the circuit (VCO) = ovate is in steady state. Insteady state fort zo The switch way closed. The circuit the capacitor ac, as opencirant. The circuit becomes :( Vo Cao) = 5volto Au sv th 2 or 1666) r=Rc. 22x12 sec .. Vo ct) » (vocal) + [4610) -voc)] étke} vols :: Vock) = 5+(0-géta boly Voch- 9.500.55 [ : volt) - 5 (1-east) wat charge across the capaciter i Q : C Volt). :Q= 2+5(1-est, coulombs

Q: 10 (1-10st) coluomas . a) The charge a across the capacitor at time t:03, Q..3 10(-2056803) =10 (1-2005) = 10 x043929 1 2.3.-1.3929 colocombs I (6) voltage across the capacitor at t: 0.3 is, You - Bos. 4.3999 I : Vou3 = 0.6965 volled o the charge a across the capacitor at t oo, Qor a 10(1-2105408) : 10 (1-2013) Qo6 e 2.5918 columbs