How Do You Calculate Instantaneous Rate of Change in an Electrical Circuit?

AI Thread Summary
To calculate the instantaneous rate of change in an electrical circuit, one must find the derivative of the current function C=(3s^3-s^2+5s)/(s^3+10) with respect to time s. The average rate of change between two time points can be determined using the formula (y2-y1)/(x2-x1), which was correctly applied in the discussion. For the instantaneous rate of change, the derivative dC/ds is essential, and it represents the limit of the average rate of change as the interval approaches zero. Understanding derivatives is crucial for solving these types of problems, especially with complex rational functions.
ArielM
Messages
2
Reaction score
0
Hi everyone, i am new to this website and i would like to ask one question that i don't quite get.
we have started a new topic in class about rates of change


Homework Statement


An Electrical current in a cicruit varies with time according to C=(3s^3-s^2+5s)/(S^3+10)
where currenct is "C" and time is "s" in seconds.

a) find the average rate of change from 0.75 seconds to 1.5 second
b)find the instantanious rate of change at 1.5 second.
c)Identify any vertical asymptotes.

Homework Equations





The Attempt at a Solution


I have managed to solved part a by substituting the values 0.75 and 1.5 to the equation.
i then took both answers and found the average rate of change by the formula y2-y1/x2-x1 (correct me if I am wrong)

as for finding the instanatnious rate of change - i am completley clueless :(
Thanks in advance !

Ariel Melichovich
 
Physics news on Phys.org
Welcome to PF!

Hi Ariel! Welcome to PF! :smile:
ArielM said:
n Electrical current in a cicruit varies with time according to C=(3s^3-s^2+5s)/(S^3+10)
where currenct is "C" and time is "s" in seconds.
…
as for finding the instanatnious rate of change - i am completley clueless :(

Instantaneous rate of change is the derivative, dC/ds. :smile:
 


tiny-tim said:
Hi Ariel! Welcome to PF! :smile:


Instantaneous rate of change is the derivative, dC/ds. :smile:

Thank you for your reply !
however, i am not quite sure what does the term 'd' mean. is that the derivative?

can the form (x,x+h) be apllied to this question where at the end i divide the equation by "h"?

Thanks again !
 
If you do not know how to find a derivative, then you cannot do this problem. The derivative is the "instantaneous rate of change". But from what you say, you seem to have heard of the basics of the derivative: it is the limit, as h goes to 0, of the average rate of change from x to x+ h. However, for the rational function you have, that is going to be a difficult algebraic calculation.

Your calculation of the average rate of change is correct
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Similar threads

Instantaneous and Average Rate of Change of f(x) | Interval (0,3)
Replies
3
Views
2K
Student Loan Payment Calculation and Effective Interest Rate Analysis
Replies
14
Views
7K
Flow Rate and Temperature Relationship in Air Change Calculations
Replies
1
Views
2K
How Do You Calculate the Flow Rate of Oxygen in a Pressurized System?
Replies
13
Views
3K
Biology How Do Stoichiometric Coefficients Affect Reaction Rates?
Replies
3
Views
2K
Why Doesn't the Flow Rate Change When a Vane is Moving in a Pipe?
Replies
11
Views
2K
I How do you calculate the cool-down rate of the Universe?
Replies
7
Views
2K
Solving Problems: Rates of Change and Value Adjustments in Math
Replies
7
Views
2K
RC circuit - Rate o'energy dissipated = rate o'energy stored
Replies
8
Views
3K
How Do You Calculate the Average Rate of Change for the Function g(t)?
Replies
2
Views
5K

Hot Threads

Recent Insights

Back
Top