# Confusion - Diff Eq for a Circuit? What does my professor mean?

• twotaileddemon
In summary, the conversation is about deriving a differential equation for the current in a series circuit with a battery, resistor, and inductance. The individual is confused about the notation used for the resistance and inductance, but eventually sets up the differential equation and is prompted to solve it with given initial conditions. The individual is unsure about the solution and seeks clarification.
twotaileddemon

## Homework Statement

My professor wants us to derive a differential equation for the current in a circuit.

The circuit has a battery with voltage E, resistor with resistance (iR)??, and inductance L. It's in series.

## The Attempt at a Solution

What REALLY confuses me are these things:

Why iR instead of R? Is the i supposed to represent current? Then why is it given for the resistance and not inductance? I don't think it could be a complex number.. it just wouldn't make sense.

Anyway, I assumed she meant R instead of iR. Then I set up a diff eq like this:

i(t)*R + L(d/dt)i(t) = 0
after a bit of math, I got
d(i(t))/i(t) = -(R/L)dt
and integrating some more math...
i(t) = Cexp(-(R/L)t) where C is some constant.
okay, that's fine. It seems to make sense to me

But then she wants us to solve it if i(0) = 0 and i(t=0) = 0.

First of all.. isn't she saying the exact same thing twice? i(0) = i(t=0) I'm guessing?
And second of all... according to my equation, i(0) = Cexp(0) = 0 implies C = 0, or that the whole expression is 0. How do I solve the differential equation if C = 0 exactly? Or does it only have a solution of 0?

Any clarification could help. Thanks!

Shouldn't it be

E = i(t)R+ Ldi/dt

ah, okay. that makes more sense. I should be able to figure something out - thanks!

## 1. What is "Confusion - Diff Eq for a Circuit"?

"Confusion - Diff Eq for a Circuit" refers to a topic in electrical engineering that involves using differential equations to analyze and understand the behavior of circuits. It can be a complex and challenging subject, but it is a fundamental aspect of circuit analysis.

## 2. How is "Confusion - Diff Eq for a Circuit" different from regular circuit analysis?

"Confusion - Diff Eq for a Circuit" focuses specifically on using differential equations to analyze circuits, while regular circuit analysis may use other methods such as Kirchhoff's laws or Thevenin's theorem. Differential equations allow for a more detailed and accurate analysis of complex circuits.

## 3. Why is "Confusion - Diff Eq for a Circuit" important to understand?

Understanding "Confusion - Diff Eq for a Circuit" is important because it allows for a deeper understanding of circuit behavior and can help in designing and troubleshooting complex circuits. It is also a necessary skill for many electrical engineering applications.

## 4. How can I better understand "Confusion - Diff Eq for a Circuit"?

To better understand "Confusion - Diff Eq for a Circuit," it is important to have a strong foundation in calculus and differential equations. It can also be helpful to practice solving problems and to seek help from professors, tutors, or online resources.

## 5. What does my professor mean by "Confusion - Diff Eq for a Circuit"?

When your professor refers to "Confusion - Diff Eq for a Circuit," they are most likely talking about the concept of using differential equations to analyze circuits. They may also be referring to a specific assignment or topic related to this concept in your course.

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