rl_rc_problem1

# rl_rc_problem1 - Sample problems Topic RC and RL circuits...

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Sample problems Topic: RC and RL circuits Statement of problem In the circuit shown in the figure, the switch has been in position a for a long time. At t=0, it moves instantaneously from a to b. (a) Find 0 () vt for 0 t . (b) What is the total energy delivered to the 1 k Ω resistor? (c) How many time constants does it take to deliver 95% of the energy found in (b)? Solution (a) At t=0, the steady state of the circuit is 2.5 mA 16 k Ω 4 k Ω (0) L i The steady current (0) L i is also the initial current for t>0. By KCL, it is 16 (0) 2.5 2 16 4 L k im A m A kk Ω =− × Ω+ Ω At t=0, the switch turns to position b, so the circuit is like 120 mH 0 v + 1 k Ω 60 mH (0) L i The PARALLEL inductance in this circuit is 120 60 120 / /60 40 120 60 mH mH mH mH mH mH mH × == + Therefore the time constant for this RL circuit is

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rl_rc_problem1 - Sample problems Topic RC and RL circuits...

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