Explanation Given: The electromotive force is applied to an RC-series is 100 -volt. The resistance is 200 ohms and the capacitance is 10 − 4 farad. Procedure used: 1. Write the circuit equation. 2. Find the integrating factor. 3. Obtain the final solution of differential equation. 4. Substitute the condition for obtain the constant value. Calculation: Consider the RC-series, R d q d t + 1 C q = E ( t ) (1) Here, d q d t is the current i , R is the resistance, C is the capacitance, q is the charge and E ( t ) is electromotive force. Substitute 200 for R , 10 − 4 for C and 100 for E ( t ) in equation (1). 200 d q d t + 1 10 − 4 q = 100 d q d t + 50 q = 0.5 . (2) The solution of the differential equation is, q ( I .F ) = ∫ 0.5 ( I .F ) d t + c (3) Obtain integrating factor of differential equation in equation (2). I .F= e ∫ 50 d t I .F= e 50 t Substitute e 50 t for I .F in equation (3) and integrate. q ( e 50 t ) = ∫ 0.5 ( e 50 t ) d t + c q ( e 50 t ) = 1 100 e 50 t + c (4) Substitute 0 for t and 0 for q in equation (4)

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ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 2.7, Problem 31E

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The charge q(t) on the capacitor if q(0)=0 and determine the current i(t).

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Chapter 2.7, Problem 30E

Chapter 2.7, Problem 32E

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Basic Differentiation Rules For Derivatives; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=IvLpN1G1Ncg;License: Standard YouTube License, CC-BY

The charge q ( t ) on the capacitor if q ( 0 ) = 0 and determine the current i ( t ) .

Solution Summary: The author analyzes the electromotive force applied to an RC-series.

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The charge q(t) on the capacitor if q(0)=0 and determine the current i(t).

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Chapter 2 Solutions