(a) Explanation Given: I ( 0 ) = 0 E = 15 volts R = 10 ohms L = 5 henries Calculation: Electrical circuit having a resistance, R = 10 ohms , an inductance, L = 5 henries , and an EMF E . Due to this EMF, a current flows in the circuit. According to Kirchhoff’s voltage law, if the circuit is closed then the applied voltage is equal to the sum of voltage drop in the rest of the circuit. Thus this means a current I ( t ) that flows in the circuit at time t must satisfy the linear differential equation E = L d I d t + R I d I d t + 10 5 I = E 5 d I d t + 2 I = E 5 Here, P ( t ) = 2 , Q ( t ) = E 5 The integrating factor is- I . F . = e ∫ 2 d t = e 2 t Thus the general solution is- I ( t ) × e 2 t = ∫ E 5 × e 2 t d t …… (1) Now, = E 5 ( e (b) To determine To find: the current I ( t ) in the circuit at time t

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J

Publisher: Kendall Hunt Publishing

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Chapter 7.6, Problem 53PS

(a)

To determine

To find: the current I(t) in the circuit at time t

(b)

To determine

To find: the current I(t) in the circuit at time t

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Chapter 7.6, Problem 52PS

Chapter 7.6, Problem 54PS

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Chapter 7 Solutions

Student's Solution and Survival Manual for Calculus

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the current I ( t ) in the circuit at time t

Solution Summary: The author calculates the current I(t) in the circuit at time t.

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To find: the current I(t) in the circuit at time t

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