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C20-activities

# C20-activities - ACTIVITY 20-1 1 k ACTIVITY 20-1 1 k vin =...

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1 ACTIVITY 20-1 in v 5u(t) = 1 k Ω 1 F μ C v + First Order Circuit Switched DC Input 0 (t t )/ C CSS C0 CSS v (t) v (v v )e τ = + C0 v 0 V = CSS v 5 V = t C v (t) 5(1 e ) t 0 τ = RC 1 msec τ = = ACTIVITY 20-1 in v 5u(t) = 1 k Ω 1 F μ C v + C in Find Differential Equation Relating v (t) to v ACTIVITY 20-1 in v 5u(t) = 1 k Ω 1 F μ C v + C R in v v v + = R v + R v iR = C dv i C dt = i C C in dv v RC v dt + = C C in dv v v dt RC RC + = C v (0 ) 0 + = ACTIVITY 20-1 C C in dv v v dt RC RC + = C C dv v 5u(t) dt RC RC L L + = in v 5u(t) = ( ) C C C V (s) 5 1 sV (s) v (0 ) RC RC s + = ( ) C C C0 V (s) 5 sV (s) v RC sRC + = Algebraic Equation ACTIVITY 20-1 ( ) C C C0 V (s) 5 sV (s) v RC sRC + = C C0 1 5 V (s) s v RC sRC + = + ( ) ( ) C0 C v 5 RC V (s) s s 1 RC s 1 RC = + + + ACTIVITY 20-1 ( ) ( ) C0 C v 5 RC V (s) s s 1 RC s 1 RC = + + + ( ) ( ) 1 2 A A 5 RC s s 1 RC s s 1 RC = + + + ( ) 1 s 0 5 RC A 5 s 1 RC = = = + 2 1 s RC 5 RC A 5 s =− = = −

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