An electric current flowing in a circuit (consisting of a battery ofV volts and a resistor of R ohms connected in series), satisfiesdIdt= −k (I −b)for some constants k and b with k > 0. Initially, I(0) = 0 and I(t)approaches a maximum level VRas t → ∞.(a) What is the value of b?b =(b) Find a formula for I(t) in terms of k, V, and R.I(t) =(c) What percent of its maximum value does I(t) reach at timet =7k?
An electric current flowing in a circuit (consisting of a battery ofV volts and a resistor of R ohms connected in series), satisfiesdIdt= −k (I −b)for some constants k and b with k > 0. Initially, I(0) = 0 and I(t)approaches a maximum level VRas t → ∞.(a) What is the value of b?b =(b) Find a formula for I(t) in terms of k, V, and R.I(t) =(c) What percent of its maximum value does I(t) reach at timet =7k?
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
Related questions
Question
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
dt
= −k (I −b)
for some constants k and b with k > 0. Initially, I(0) = 0 and I(t)
approaches a maximum level V
R
as t → ∞.
(a) What is the value of b?
b =
(b) Find a formula for I(t) in terms of k, V, and R.
I(t) =
(c) What percent of its maximum value does I(t) reach at time
t =
7
k
?
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