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lecture25 - Find the current through each component and the...

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Self-Inductance and Circuits Self-Inductance and Circuits Inductors in circuits RL circuits
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Inductors in Series and Parallel L T = L 1 +L 2 …. 1/L T = 1/L 1 + 1/L 2
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Self-Inductance Self-Inductance dt dI L L - = ε I 2 2 1 LI U L = Potential energy stored in an inductor: Self-induced emf:
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RL circuits: current increasing RL circuits: current increasing Theswitch is closed at t =0; Find I (t). - = - = = - - I R L R L IR dt dI IR dt dI L ε ε ε 0 ε L R I Kirchoff’s loop rule:
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Solution Solution R L = τ TimeConstant: Note that H/ = seconds Ω (show as exercise!) ( 29 τ ε / 1 ) ( t e R t I - - =
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0 1 τ 2 τ 3 τ 4 τ 63% ε /R I t Time Constant: Current Equilibrium Value: R L = τ ( 29 τ ε / 1 ) ( t e R t I - - = R I ε =
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Example 1 Calculate the inductancein an RL circuit in which R=0.5 and thecurrent increases to onefourth of its final value in 1.5 sec.
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L R I RL circuits: current decreasing Assumetheinitial current I 0 is known. Find the differential equation for I(t) and solveit.
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I t 0 τ τ 2 τ 3 τ 4 τ 0.37 I 0 I o / o ( ) t I t I e τ - = Current decreasing: TimeConstant: R L = τ
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Example 2: Example 2: 12 V 200 mH 50k Ω 6 Ω I 3 I 2 I 1 a) Theswitch has been closed for a long time.
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Unformatted text preview: Find the current through each component, and the voltage across each component. a) The switch is now opened. Find the currents and voltages just afterwards. Solution LC circuits LC circuits (Extra! – not on test/exam) (Extra! – not on test/exam) The switch is closed at t =0; Find I (t). C L I Which can be written as (remember, P=VI): +-Looking at the energy loss in each component of the circuit gives us: E L +E C =0 = + = + C Q dt dI L I C Q dt dI LI Solution RLC circuits RLC circuits (Extra! – not on test/exam) (Extra! – not on test/exam) The switch is closed at t =0; Find I (t). C L R I Which can be written as (remember, P=VI=I 2 R): +-Looking at the energy loss in each component of the circuit gives us: E L +E R +E C =0 2 = + + = + + C Q IR dt dI L I C Q R I dt dI LI Solution...
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