Which is the constant of differentiation?

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Homework Help Overview

The discussion revolves around differentiation in the context of electrical circuits, specifically focusing on the differentiation of terms involving current (I), resistance (R), and potentially other constants. Participants are exploring the implications of treating certain variables as constants while differentiating with respect to time.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are questioning why certain terms are treated as constants during differentiation and are exploring the implications of differentiating with respect to time. There is a focus on understanding the roles of I, R, and other constants in the differentiation process.

Discussion Status

The discussion is active, with participants providing insights into the nature of constants in the context of differentiation. Some have suggested using the product rule for differentiation, indicating a potential direction for further exploration. There is an ongoing examination of the assumptions regarding which variables can be treated as constants.

Contextual Notes

Participants note that L, R, and C are constants in the context of the problem, while I is not treated as a constant. The original equation referenced may provide additional context for understanding the differentiation process.

Calpalned
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When the textbook differentiated with respect to time, I see that the middle term is R(dI/dt). Why can't it be I(dR/dt)? When I differentiate, how do I know which letter to differentiate?
3. The Attempt at a Solution
2. Homework Equations
1. Homework Statement
 
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Calpalned said:
View attachment 90516
When the textbook differentiated with respect to time, I see that the middle term is R(dI/dt). Why can't it be I(dR/dt)? When I differentiate, how do I know which letter to differentiate?

The Attempt at a Solution


Homework Equations


Homework Statement

L, R, and C are constants. You are differentiating with respect to time and the constants don't vary.
 
Calpalned said:
View attachment 90516
When the textbook differentiated with respect to time, I see that the middle term is R(dI/dt). Why can't it be I(dR/dt)? When I differentiate, how do I know which letter to differentiate?

The Attempt at a Solution


Homework Equations


Homework Statement

Why did you ignore the template? You even went through the trouble to change the font color.

To answer your question:

R is a constant just like L and C. You had no objection to treating them as constants.
 
LCKurtz said:
L, R, and C are constants. You are differentiating with respect to time and the constants don't vary.
I see... If I look at the original equation (1.2) has ##\frac{dI}{dt}## and that tells me that I is not a consant?
 
Calpalned said:
I see... If I look at the original equation (1.2) has ##\frac{dI}{dt}## and that tells me that I is not a consant?
Actually, it helps to understand something of the physics behind this problem.

V is voltage or emf. I is current.
 
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SammyS said:
Actually, it helps to understand something of the physics behind this problem.
The example was on differential equations in general, so the textbook didn't give me background information on the physics.
 
Calpalned said:
The example was on differential equations in general, so the textbook didn't give me background information on the physics.
You could use the product rule, differentiating the product RI w.r.t. time. What result would you get?
 

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