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An electric current flowing in a circuit (consisting of a battery of V volts and a resistor of Rohms connected in series), satisfies dI = -k (I – b) dt for some constants k and b with k > 0. Initially, I(0) 0 and I(t) approaches a maximum level as t → 0. (a) What is the value of b? 6 = (b) Find a formula for I(t) in terms of k, V, and R. I(t) =D (c) What percent of its maximum value does I(t) reach at time t = ? %

An electric current flowing in a circuit (consisting of a battery of V volts and a resistor of Rohms connected in series), satisfies dI = -k (I – b) dt for some constants k and b with k > 0. Initially, I(0) 0 and I(t) approaches a maximum level as t → 0. (a) What is the value of b? 6 = (b) Find a formula for I(t) in terms of k, V, and R. I(t) =D (c) What percent of its maximum value does I(t) reach at time t = ? %

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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An electric current flowing in a circuit (consisting of a battery of V volts and a resistor of R ohms connected in series), satisfies dI = -k (I – b) dt for some constants k and b with k > 0. Initially, I(0) = 0 and I(t) approaches a maximum level as t → 0. (a) What is the value of b? (b) Find a formula for I(t) in terms of k, V, and R. I(t) =O (c) What percent of its maximum value does I(t) reach at time t = ? %
Transcribed Image Text:An electric current flowing in a circuit (consisting of a battery of V volts and a resistor of R ohms connected in series), satisfies dI = -k (I – b) dt for some constants k and b with k > 0. Initially, I(0) = 0 and I(t) approaches a maximum level as t → 0. (a) What is the value of b? (b) Find a formula for I(t) in terms of k, V, and R. I(t) =O (c) What percent of its maximum value does I(t) reach at time t = ? %
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