Explanation The formula for the current in the steady is given by i = V R . If the current reaches half of its steady state, then i = 1 2 ( V R ) . Consider the equation d i d t + R L i = V L . Compare the equation with the standard form d y d x + P ( x ) y = Q ( x ) . Here, P ( t ) = R L and Q ( t ) = V L . Evaluate the integrating factor as follows. v ( t ) = e ∫ p ( t ) d t = e ∫ R L d t = e R t L Thus, the integrating factor is v ( t ) = e R t L . Solve the equation d i d t + R L i = V L as follows. i = 1 v ( t ) ∫ v ( t ) Q ( t ) d t = 1 e R t L ∫ e R t L ( V L ) d t = 1 e R t L [ L R e R t L ( V L ) + C ]

Thomas' Calculus Format: Unbound (saleable) With Access Card

14th Edition

ISBN: 9780134768762

Author: Hass, Joel R.^heil, Christopher D.^weir, Maurice D.

Publisher: Prentice Hall

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Question

Chapter 9.2, Problem 25E

To determine

The time taken by the current to reach half of its steady state after the switch in the RL circuit is closed.

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Chapter 9.2, Problem 24E

Chapter 9.2, Problem 26E

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Thomas' Calculus Format: Unbound (saleable) With Access Card

Ch. 9.1 - Prob. 1E Ch. 9.1 - In Exercises 1–4, match the differential equations...Ch. 9.1 - In Exercises 1–4, match the differential equations...Ch. 9.1 - In Exercises 1–4, match the differential equations...Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E

Ch. 9.1 - Prob. 11E Ch. 9.1 - Prob. 12E Ch. 9.1 - Prob. 13E Ch. 9.1 - In Exercises 13 and 14, consider the differential...Ch. 9.1 - Prob. 15E Ch. 9.1 - Prob. 16E Ch. 9.1 - Prob. 17E Ch. 9.1 - Prob. 18E Ch. 9.1 - Prob. 19E Ch. 9.1 - Prob. 20E Ch. 9.1 - Prob. 21E Ch. 9.1 - Prob. 22E Ch. 9.1 - Prob. 23E Ch. 9.1 - Prob. 24E Ch. 9.1 - Prob. 25E Ch. 9.1 - Prob. 26E Ch. 9.2 - Prob. 1E Ch. 9.2 - Solve the differential equations in Exercises...Ch. 9.2 - Prob. 3E Ch. 9.2 - Prob. 4E Ch. 9.2 - Prob. 5E Ch. 9.2 - Prob. 6E Ch. 9.2 - Prob. 7E Ch. 9.2 - Prob. 8E Ch. 9.2 - Prob. 9E Ch. 9.2 - Prob. 10E Ch. 9.2 - Prob. 11E Ch. 9.2 - Prob. 12E Ch. 9.2 - Prob. 13E Ch. 9.2 - Prob. 14E Ch. 9.2 - Prob. 15E Ch. 9.2 - Prob. 16E Ch. 9.2 - Prob. 17E Ch. 9.2 - Prob. 18E Ch. 9.2 - Solve the initial value problems in Exercises...Ch. 9.2 - Prob. 20E Ch. 9.2 - Prob. 21E Ch. 9.2 - Prob. 22E Ch. 9.2 - Prob. 23E Ch. 9.2 - Prob. 24E Ch. 9.2 - Prob. 25E Ch. 9.2 - Prob. 26E Ch. 9.2 - Prob. 27E Ch. 9.2 - Prob. 28E Ch. 9.2 - Prob. 29E Ch. 9.2 - Prob. 30E Ch. 9.2 - Prob. 31E Ch. 9.2 - Prob. 32E Ch. 9.3 - Prob. 1E Ch. 9.3 - Prob. 2E Ch. 9.3 - Prob. 3E Ch. 9.3 - Prob. 4E Ch. 9.3 - Prob. 5E Ch. 9.3 - Prob. 6E Ch. 9.3 - Prob. 7E Ch. 9.3 - Prob. 8E Ch. 9.3 - Prob. 9E Ch. 9.3 - Prob. 10E Ch. 9.3 - Prob. 11E Ch. 9.3 - Prob. 12E Ch. 9.3 - Prob. 13E Ch. 9.3 - Prob. 14E Ch. 9.3 - Fertilizer mixture A tank contains 100 gal of...Ch. 9.3 - Carbon monoxide pollution An executive conference...Ch. 9.4 - Prob. 1E Ch. 9.4 - Prob. 2E Ch. 9.4 - Prob. 3E Ch. 9.4 - Prob. 4E Ch. 9.4 - In Exercises 1–8, Identify the equilibrium values....Ch. 9.4 - Prob. 6E Ch. 9.4 - Prob. 7E Ch. 9.4 - Prob. 8E Ch. 9.4 - Prob. 9E Ch. 9.4 - Prob. 10E Ch. 9.4 - Prob. 11E Ch. 9.4 - Prob. 12E Ch. 9.4 - Prob. 13E Ch. 9.4 - Prob. 14E Ch. 9.4 - Prob. 15E Ch. 9.4 - Prob. 16E Ch. 9.4 - Prob. 17E Ch. 9.4 - The spread of information Sociologists recognize a...Ch. 9.4 - Prob. 19E Ch. 9.4 - Prob. 20E Ch. 9.5 - Prob. 1E Ch. 9.5 - Prob. 2E Ch. 9.5 - Prob. 3E Ch. 9.5 - Prob. 4E Ch. 9.5 - Consider another competitive-hunter model defined...Ch. 9.5 - Prob. 6E Ch. 9.5 - Prob. 7E Ch. 9.5 - Prob. 8E Ch. 9.5 - Prob. 9E Ch. 9.5 - Prob. 10E Ch. 9.5 - Prob. 11E Ch. 9.5 - Prob. 12E Ch. 9.5 - Prob. 13E Ch. 9.5 - Prob. 14E Ch. 9 - Prob. 1GYR Ch. 9 - Prob. 2GYR Ch. 9 - Prob. 3GYR Ch. 9 - Prob. 4GYR Ch. 9 - Prob. 5GYR Ch. 9 - What is an orthogonal trajectory of a family of...Ch. 9 - Prob. 7GYR Ch. 9 - Prob. 8GYR Ch. 9 - Prob. 9GYR Ch. 9 - Prob. 10GYR Ch. 9 - Prob. 1PE Ch. 9 - Prob. 2PE Ch. 9 - Prob. 3PE Ch. 9 - Prob. 4PE Ch. 9 - Prob. 5PE Ch. 9 - Prob. 6PE Ch. 9 - Prob. 7PE Ch. 9 - Prob. 8PE Ch. 9 - Prob. 9PE Ch. 9 - Prob. 10PE Ch. 9 - Prob. 11PE Ch. 9 - Prob. 12PE Ch. 9 - Prob. 13PE Ch. 9 - Prob. 14PE Ch. 9 - Prob. 15PE Ch. 9 - Prob. 16PE Ch. 9 - Prob. 17PE Ch. 9 - Prob. 18PE Ch. 9 - Prob. 19PE Ch. 9 - Prob. 20PE Ch. 9 - Prob. 21PE Ch. 9 - Prob. 22PE Ch. 9 - Prob. 23PE Ch. 9 - Prob. 24PE Ch. 9 - Prob. 25PE Ch. 9 - Prob. 26PE Ch. 9 - Prob. 27PE Ch. 9 - Prob. 28PE Ch. 9 - Prob. 29PE Ch. 9 - Prob. 30PE Ch. 9 - Prob. 31PE Ch. 9 - Prob. 32PE Ch. 9 - Prob. 35PE Ch. 9 - Prob. 36PE Ch. 9 - Prob. 37PE Ch. 9 - Prob. 38PE Ch. 9 - Prob. 39PE Ch. 9 - Prob. 40PE Ch. 9 - Prob. 41PE Ch. 9 - Prob. 42PE Ch. 9 - Prob. 43PE Ch. 9 - Prob. 44PE Ch. 9 - Prob. 1AAE Ch. 9 - Prob. 2AAE Ch. 9 - Prob. 3AAE Ch. 9 - Prob. 4AAE Ch. 9 - Prob. 5AAE Ch. 9 - Prob. 6AAE Ch. 9 - Prob. 7AAE Ch. 9 - Prob. 8AAE Ch. 9 - Prob. 9AAE Ch. 9 - Prob. 10AAE

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