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# Has a case 1 b case 2 c the same l 1 2r 50 40 30 20 l

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Unformatted text preview: no t c h a ng e DIS C O NT INUO US LY BB R 20 15 10 5 0 Wh y is th e re e xp o ne ntia l b e h a vio r ? I − V = L dI dt L + VL + R τ = L/R L/R V = IR − τ = L/R L/R dI L + IR = 0 dt I (t ) = I 0e −tR / L = I 0e −t / τ L where τ = R I L VL R VBATT τ = L/R L/R Le c ture : P re le c ture : Did we m e s s up ? ? No: The resistance is simply twice as big in one case. Preflight 8 After long time at 0, moved to 1 After long time at 0, moved to 2 BB After switch moved, which case After has larger time constant? has A) Case 1 B) Case 2 C) The same L τ1 = 2R 50 40 30 20 L τ2 = 3R 10 0 Preflight 10 After long time at 0, moved to 1 After long time at 0, moved to 2 BB Immediately after switch moved, Immediately in which case is the voltage across the inductor larger? across A) Case 1 After switch moved: B) Case 2 V VL1 = 2 R C) The same R Before switch moved: I = V R VL 2 = V 3R R 40 30 20 10 0 Preflight 12 After long time at 0, moved to 1 After long time at 0, moved to 2 BB After switch moved for finite time, in After which case is the current through the inductor larger? the A) Case 1 After awhile B) Case 2 I1 = Ie −t / τ C) The same 1 Immediately after: I1 = I 2 I 2 = Ie−t / τ τ1 > τ 2 2 50 40 30 20 10 0 Calculation Calculation The switch in the circuit shown has been open for a long time. At t = 0, the switch is closed. What is dIL/dt, the time rate of change of the current through the inductor immediately after switch is closed R1 V R2 L • Conceptual Analysis – – Once switch is closed, currents will flow through this 2­loop circuit. KVR and KCR can be used to determine currents as a function of time. • Strategic Analysis – Determine currents immediately after switch is closed. – Determine voltage across inductor immediately after switch is closed. – Determine dIL/dt immediately after switch is closed. R3 Calculation Calculation The switch in the circuit shown has been open for a long time. At t = 0, the switch is closed. R1 V R2 BB L IL = 0 What is IL, the current in the inductor, immediately after the switch is closed? (A) IL =V/R1 up (B) IL =V/R1 down (C) IL = 0 INDUCTORS: Current cannot change discontinuously ! Current throug...
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