Integration question (average voltage)

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Homework Help Overview

The problem involves calculating the average voltage and root mean square (r.m.s.) voltage from a voltage function represented by v = 15 sin (200πt) volts over specified time intervals. The subject area pertains to integration in the context of electrical circuits.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the method for finding the average value of a function over an interval using integration. Some express uncertainty about the integration process and whether it is necessary to integrate the function directly. Questions arise regarding the implications of integrating within specified limits and the correctness of the integration attempts.

Discussion Status

Participants are actively engaging with the problem, sharing insights about the average value formula and discussing the integration process. There is a mix of attempts to clarify the method and questions about the integration limits, indicating a productive exploration of the topic without reaching a consensus on the specific steps to take.

Contextual Notes

Some participants question the understanding of the problem and the necessity of integrating the voltage function, highlighting potential assumptions about the integration limits and the function itself.

ckeller
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Homework Statement



The voltage at a point in a circuit is represented by the function v = 15 sin (200πt) volts. Use integration methods to calculate;

(a) The average voltage between t = 5ms and t = 10ms
(b) The average voltage between t = 0 and t = 10ms
(c) The r.m.s. voltage between t = 5ms and t = 15ms


Homework Equations





The Attempt at a Solution



I'm not too sure I understand the question properly, could anyone help at all?
 
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The average value of a function f(x) over an integral [a,b] is such:

Avg = \frac{1}{b-a} \int_a^b f(x) dx

See how you can use this to help you?
 
Char. Limit said:
The average value of a function f(x) over an integral [a,b] is such:

Avg = \frac{1}{b-a} \int_a^b f(x) dx

See how you can use this to help you?

Oh yeah thanks, that is useful to know! so I don't need to integrate 15sin(200PIt)?
 
I got [15-cos(200pit)/pi + C] does that look right?

And then calculate between 5 and 10 ms
 
ckeller said:
Oh yeah thanks, that is useful to know! so I don't need to integrate 15sin(200PIt)?
Yes, you need to integrate.

Char. Limit has given you a method for finding the average of a function. That method has an integral.
 
what is wrong if you integrate the functions in the limit specified?
 
asitiaf said:
what is wrong if you integrate the functions in the limit specified?
Could you please clarify your question ?
 

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