C16-activities - ACTIVITY 16-1 R = 20 ACTIVITY 16-1 L = .5...

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1 ACTIVITY 16-1 s v y + R2 0 L. 5 H = C 111 C F, F 250 200 150 = 22 0 2 0 Characteristic Equation s 2 s 0 R1 ; 2L LC αω ++ = == ACTIVITY 16-1 2 20 20; 400 2(.5) αα = 0 12 0 10t 30t N1 2 1 C F : 150 300 ; s ,s 10, 30 y K e K e ωα ω −− = =< =− ± =− => = + Overdamped 2 Decaying Exponentials ACTIVITY 16-1 0 20t 20t 2 1 F : 200 400 s,s 20 y K e K t e α = =− =− => = + Critically Damped ACTIVITY 16-1 Decaying exponential exponentially damped ramp + 2 2 00 20t N 1 F : 250 500 10 j 20 j10 y A e cos (10t ) β αβ φ = => = = ± => = + Underdamped Sinusoid with exponentially decaying amplitude ACTIVITY 16-1 ACTIVITY 16-2a in v( t ) 10u(t) = R 1 H 1 F 400 L .1v L v + i(t) C v + Find i(t)
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2 ACTIVITY 16-2a in v( t ) 10u(t) = R 1 H 1 F 400 L .1v L v +− i(t) C v + CLR i n KVL: v v v v ++= L di vL dt = R vi R = CC 1 d t C = C i ACTIVITY 16-2a in t ) 10u(t) = R 1 H 1 F 400 L .1v L + i(t) C v + CL KCL: i i .1v = L di dt = C di ii . 1 L dt =− C i ACTIVITY 16-2a n KVL: v v v v L di dt = R R = 1 d t C = C 1d i i . 1 L ) d t Cd t in i d i (i .1L ) dt iR L v t d t −+ + = 2 in 2 dv i .1L di di d i RL C C dt dt dt dt + = ACTIVITY 16-2a 2 in 2 dv i .1L di di d i C C dt dt dt dt + = 2 in 2 dv di .1L d i i LR dt C dt C dt ⎛⎞ += ⎜⎟ ⎝⎠ 2 in 2 .1L R dv d i i 1 C dt L dt LC L dt ++ = ACTIVITY 16-2a
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C16-activities - ACTIVITY 16-1 R = 20 ACTIVITY 16-1 L = .5...

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