Assume that V (t) = V is constant and I (0) = 0. (a) Solve for I (t). (b) Show that lim t→∞ I (t) = V/R and that I (t) reaches approximately 63% of its limiting value after L/R seconds. (c) How long does it take for I (t) to reach 90% of its limiting value if R = 500 ohms, L = 4 henries, and V = 20 volts?

Assume that V (t) = V is constant and I (0) = 0. (a) Solve for I (t). (b) Show that lim t→∞ I (t) = V/R and that I (t) reaches approximately 63% of its limiting value after L/R seconds. (c) How long does it take for I (t) to reach 90% of its limiting value if R = 500 ohms, L = 4 henries, and V = 20 volts?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 18T

See similar textbooks

Related questions

Q: . Let f(x) = 5x² - 10x - 17. (a) Use limit method to find f'(x). Show all of your work. (b) Find an…

Q: For the function y = f(x) = – le'+9: %3D df at x = 4. da a. Find f'(4) = %3D b. Find a formula for a…

Q: For each of the given functions f(z), find the derivative (f)'(c) at the given point c, first…

Q: 1. Let f(x) = x² - 2x + 1. (a) Find the slope of the graph of y = f (x) at the point P = (0, 1) by…

A: Given information Function: fx=x2 -2x+1, Also, define as y=f(x)y=x2 -2x+1. Point P : 0, 1 Formula:…

Q: Suppose an arrow is shot upward on a certain planet with an intial height of 1.7 meters and an…

Q: A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the…

A: Given: Function, f(x)=150-15x Boundary conditions: u0,t=u3,t=0To find: ux,t, u42, 0.1

Q: If a space shuttle's downward acceleration is given by y"(t) = –32 ft/s², find the osition function…

Q: 10. The arclength of the graph (x, f(x)) for a function f where a ≤ x ≤ b is given by the expression…

A: given (x,f(x)) where a≤x≤b

Q: Lt) denote the length of a fish at time and assume L(0) = Lo-The von Bertalanffy equation is dL dt =…

A: Given: The Von Bertalanffy equation is dLdt=kA-L The value of A is 3 The value of length L0=0.5m…

Q: 6. A projectile is launched with an initial speed vo at an angle 0 (here 0 <0 < 7/2). The height as…

A: **As per our guidelines we are allowed to answer maximum 3 sub-parts at a time. Kindly please…

Q: If g(t)=t^2tan(t), then can the Intermediate Value Theorem be used on the interval [0, pi/4] to show…

A: If a continuous function in a domain has two domain end points and one point is above the required…

Q: a) Suppose f' (x) = sin(x² ) and f(0) = 4. Use a graph of f' (x) to decide which is larger: (i) ƒ(0)…

Q: A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the…

Q: 6. (a) Solve the equation dy dx You may leave your answer in an implicit form (i.e. you do not need…

A: (.) Given differential equation is, (.) Method of seperation of variables:A equation of…

Q: The amount of electrical resisitance (R) in a medium depends on the temperature, and for certain…

A: Determine the resistance equation by substituting k=30.

Q: Let f(x)= (200x-500) /(x+400) Find horizontal and vertical asymptotes, and zeros and sketch the…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: Assume h(x) = (f(x))3. If f1(0)= −1/2, and f(0) = 8/3, determine an equation of the line tangent to…

Q: 90. The function C(t) = K(ea – eb), where a, b, and K are positive constants and b> a, is used to…

Q: The growth rate of a particular species of fish is modeled by G(x) = 0.02x (1 – 700000 where x is…

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Assume that V (t) = V is constant and I (0) = 0.
(a) Solve for I (t).
(b) Show that lim
t→∞
I (t) = V/R and that I (t) reaches approximately 63% of its limiting value after L/R seconds.
(c) How long does it take for I (t) to reach 90% of its limiting value if R = 500 ohms, L = 4 henries, and V = 20 volts?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

A bacterial culture is growing according to the logistic growth function y = 1.25 /(1 + 0.25e−0.4t)() , t ≥ 0 where y is the weight of the culture in grams and t is the time in hours. Find the weight of the culture after (a) 0 hours, (b) 1 hour, and (c) 10 hours. (d) What is the limit as t approaches infinity?
Q3. Solve in terms of Bessel's function, the ODE x²y" + xy' + ((lnx)² + ²)y=0_z=lnx.
90. The function C(t) = K(ea – eb), where a, b, and K are positive constants and b> a, is used to model the concen- tration at time t of a drug injected into the bloodstream. (a) Show that lim, C(t) = 0. (b) Find C"(t), the rate of change of drug concentration in the blood. (c) When is this rate equal to 0?
Find f(a) a=2
S(₁) = 4₁7²¹²2 r-radius √(A) = 2/5 +²³1 +20₁ r(t) Quartet find surface areas as a function of the time
Suppose that a cylindrical tank initially containing Vo gallons of water drains through a bottom hole in T minutes. Use Torricelli's law to show that the volume of water in the tank after t≤ T minutes is V = V₁ [1₁ - ( 7 )] ²³. Suppose that a water tank has a hole with area a at its bottom, from which water is leaking. Let y(t) be the depth of the water in the tank at time t, let V(t) be the volume of the water in the tank at the same time, and let A(y) be the horizontal cross-sectional area of the tank at height y. Torricelli's law states that dV dt dy = a√ a√2gy, or equivalently, A(y)- = av dt a√/2gy. Suppose that the cylindrical tank has a constant radius r. Then, A(y) = 0.
19. Joe drives north from Eugene, leaving at noon. If t is the number of hours since noon and d(t) is his position measuring north from Eugene, his velocity is given by d'(t) = t³ – 11t2 + 24t mi - for 0
1. Consider the following sentences: “You can approximate your instantaneous velocity at a point intime by finding your average velocity over a short interval containing that time. As you make theinterval shorter, your approximation improves.” Now explain why this formula for instantaneousvelocity makes sense:v(a) = limh→0f(a + h) − f(a)h.
A tank initially contains so lb of salt dissolved in 400 gal of water, where so is some positive number. Starting at time t=0, water containing 2 lb of salt per gallon enters the tank at a rate of 8 gal/min, and the well-stirred solution leaves the tank at the same rate. Letting c(t) be the concentration of salt in the tank at time t, show that the limiting concentration that is, lim c(t)-is 2 lb/gal. 1→∞0 Write an equation for the rate of salt (in lb/min) that flows into the tank, where t is the time in minutes. Flow in
A tank initially contains so lb of salt dissolved in 400 gal of water, where so is some positive number. Starting at time t=0, water containing 2 lb of salt per gallon enters the tank at a rate of 8 gal/min, and the well-stirred solution leaves the tank at the same rate. Letting c(t) be the concentration of salt in the tank at time t, show that the limiting concentration that is, lim c(t)-is 2 lb/gal. 00+1 Write an equation for the rate of salt (in lb/min) that flows into the tank, where t is the time in minutes. Flowin = 16 Write an equation for the rate of salt (in lb/min) that flows out of the tank, where t is the time in minutes. Flow out =
6. (a) Solve the equation dy dx You may leave your answer in an implicit form (i.e. you do not need to solve for y). = = x²y-²e- (b) Determine the explicit solution which satisfies the condition that y(0) = 1. (c) Find the (exact) limit lim y(x) for your solution. H48
Show that f(x)g(x) = (x – a)" Cmdn-m n'=0 m=0