Vb Vb dI R + I L dt L eeeeeee (a) Show that when the switch S is closed, the time-dependence of the current is governed by the following first-order differential equation: = L (b) Follow the methods used in class to solve this differential equation and find an expression for I(t). Assume that the switch is closed at time t = 0 and I(0) = 0. For the RC circuit, the relevant charging time constant was 7 = RC. What is the time constant that determines how the current increases after the switch is closed? (c) What is the time dependence of the voltage across the inductor after the switch is closed? (d) Sketch I(t) and V₁(t) as a function of time. Indicate the maximum values of I and V₁ and their values when t = 7 where 7 is the time constant you found in part (b).

Vb Vb dI R + I L dt L eeeeeee (a) Show that when the switch S is closed, the time-dependence of the current is governed by the following first-order differential equation: = L (b) Follow the methods used in class to solve this differential equation and find an expression for I(t). Assume that the switch is closed at time t = 0 and I(0) = 0. For the RC circuit, the relevant charging time constant was 7 = RC. What is the time constant that determines how the current increases after the switch is closed? (c) What is the time dependence of the voltage across the inductor after the switch is closed? (d) Sketch I(t) and V₁(t) as a function of time. Indicate the maximum values of I and V₁ and their values when t = 7 where 7 is the time constant you found in part (b).

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter33: Inductors And Ac Circuits

Section: Chapter Questions

Problem 16PQ: In Figure 33.9A (page 1052), the switch is closed at a at t = 0. Find an expression for the power...

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