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rl_rc_problem3 - Sample problems Topic RC and RL circuits...

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Sample problems Topic: RC and RL circuits Statement of problem The switch in the circuit in the figure has been in position a for a long time. 8 mA 27 k Ω 33 k Ω a b 0 t = 0.25 F μ 3 k Ω 2 k Ω 4 k Ω 0 i At t=0, the switch is thrown to position b. (a) Find 0 ( ) i t for t>0. (b) What percentage of the initial energy stored in the capacitor is dissipated in the 4 k Ω resistor 250 s μ after the switch has been thrown? Solution (a) Prior to t=0, the circuit looks like 8 mA 27 k Ω 33 k Ω a 0.25 F μ First, the initial voltage on the capacitor is calculated by KVL (0) 8 (27 / /33 ) 118.8 c v mA k k V = × Ω Ω = Then after t=0, the circuit looks like b 0.25 F μ 3 k Ω 2 k Ω 4 k Ω 0 i (0) C v + The time constant for the RC circuit is (3 / /(2 4 )) 0.25 0.5 k k k F ms τ μ = Ω Ω + Ω × = Therefore, for t>0, the voltage on the capacitor is ( ) (0)exp( / ) 118.8exp( 2000 )( ) c c v t v t t V τ =
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