rl_rc_problem2 - 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 and 2 0 v = . 2 v + 1 v + 4.7 k Ω 5 k Ω 2 F μ 8 F a b 0 t = i 75 V At t=0, the switch is thrown to position b. Calculate (a) i , 1 v and 2 v for 0 t . (b) The energy stored in the capacitor at t=0. (c) The energy trapped in the circuit and the total energy dissipated in the 5 k Ω resistor if the switch remains in position b indefinitely. Solution (a) Prior to t=0, the circuit can be modeled as follows 1 v + 4.7 k Ω 2 F a 75 V Capacitors are open circuit at steady state, so at t=0 1 (0) 75 vV = After the switch is turned to position b, the circuit will discharge via the two SERIES capacitors. The series capacitance is 28 1.6 FF CF μμ × == + So the time constant is 51 . 6 8 R Ck Fm s τ Ω × = The circuit looks as follows 1 (0) v + 5 k Ω 1.6 F b i The current in the loop is also the current flowing through the resistor. By KVL 1 (0) 75 exp( / ) exp( / 8 ) 15exp( 125 )( ) 5 v V it t m s t m A Rk =− = Ω
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This note was uploaded on 10/30/2011 for the course EE 215 taught by Professor Unknown during the Spring '05 term at University of Washington.

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rl_rc_problem2 - Sample problems Topic: RC and RL circuits...

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