# 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
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 The switch 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:
Solution Solution R L = τ Time Constant: 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 =
Example 1 Calculate the inductance in an RL circuit in which R=0.5 and the current increases to one fourth of its final value in 1.5 sec.

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L R I RL circuits: current decreasing Assume the initial current I 0 is known. Find the differential equation for I(t) and solve it.
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: Time Constant: 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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