Lecture_13 - t=0. Find v(t) for t ≥ 0. BME 311 Network...

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1 BME 311 Network Theory John X.J. Zhang, UT Austin 1 First-order Circuits • Characterized by a first-order differential equation RC, RL Two way of excitations • Source-free • Independent sources (dc, sinusoidal, exponential) τ t RC t e V e V t v = = 0 0 ) ( Where, = RC ? BME 311 Network Theory John X.J. Zhang, UT Austin 2 Natural Response of RC Circuit Natural response: the circuit response with no external sources of excitation Time constant τ : the time required for the response to decay to a factor of 1/e or 36.8% of its initial value ± 5 τ : “fully” charges or discharged ± v(t+ ) = v(t)/e = 0.368 v(t) t RC t e V e V t v = = 0 0 ) ( Where, = RC
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2 BME 311 Network Theory John X.J. Zhang, UT Austin 3 • Time constant τ (cont.) ± Initial rate of decay ± Smaller τ Æ faster response (charge or discharge) BME 311 Network Theory John X.J. Zhang, UT Austin 4 • Find the time constant for each RC circuit.
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3 BME 311 Network Theory John X.J. Zhang, UT Austin 5 • The switch has been closed for a long time, and it opens at
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Unformatted text preview: t=0. Find v(t) for t ≥ 0. BME 311 Network Theory John X.J. Zhang, UT Austin 6 A e i t 4 2 . − = For the following circuit: 4 BME 311 Network Theory John X.J. Zhang, UT Austin 7 • Given the circuit in the following figure, find v(t) for v c (t) = (10+5t) V. BME 311 Network Theory John X.J. Zhang, UT Austin 8 The Source-Free RL Circuit • The inductor has an initial current i(0)=I , at t=0 . Find circuit response i(t). What is the energy dissipated in the resistor ? 5 BME 311 Network Theory John X.J. Zhang, UT Austin 9 Natural Response of RL Circuit τ t e I t i − = ) ( R L = BME 311 Network Theory John X.J. Zhang, UT Austin 10 • Find the time constant for each of the circuits. 6 BME 311 Network Theory John X.J. Zhang, UT Austin 11 • Find the value R for which the steady-state energy stored in the inductor will be 1 J ....
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This note was uploaded on 09/28/2009 for the course BME 311 taught by Professor Zhang during the Spring '08 term at University of Texas at Austin.

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Lecture_13 - t=0. Find v(t) for t ≥ 0. BME 311 Network...

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