Help Needed for Solving Electrical Circuit Problem

In summary, the correct expression for ##I(t)## is ##i(t)=0.06e^{-(R/L)t}## and by setting ##i(t^*)=35\cdot 10^{-3} A##, the correct value can be obtained. The mistake was using the wrong formula and not accounting for the absence of a battery in the "new" circuit.
  • #1
lorenz0
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Homework Statement
At the beginning the switch c of the circuit is in position 1. At t=0, it switches to position 2.
(1) Find ##I(0).## (2) Find ##t*## such that ##I(t*)=35mA.##
Relevant Equations
##I(t)=I(0)(1-e^{(-R/L)t)},\ I(0)=\frac{V}{R}##
What I have done:

(1) ##I(0)=\frac{V}{R}=\frac{1.5}{25}A=0.06 A.##

(2) By setting ##I(t*)=0.06(1-e^{-(35/0.4)t*})=35 mA## we get ##t*\approx 0.01 s##

What I have done seems correct to me, but the result for part (2) should be different.
I would be grateful if someone could point out to me where I have made a mistake.
 

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  • #2
You have the wrong expression for ##I(t)##. It does not predict that ##I(0) =0.06## A. What is the correct expression to use?

Also, please enter the exponent correctly in LaTeX as e^{-Rt/L} to render as ##e^{-Rt/L}##. Or you could write it as ##\exp(-R t/L)##.
 
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  • #3
lorenz0 said:
(2) By setting ##I(t*)=0.06(1-e^((-35/0.4)t*))=35 mA## we get ##t*=\approx 0.01 s##
You have used the wrong formula! Can you see why? If you can't, click the spoiler for a hint:
When the switch has been at position 2 for a long time, do you expect the current through the inductor to be 0.06A?

Also, here's a LaTeX formatting hint:
e^(-R/L)t gives: ##e^(-R/L)t## (yuchy)
but
e^{(-R/L)t} gives: ##e^{(-R/L)t}## (slightly yuchy)
Another alternative is:
e^{-(R/L)t} gives: ##e^{-(R/L)t}## (almost not yuchy)

For zero-yuchiness, I would define the time-constant as ##\tau = \frac L R##. Then
e^{-\frac t {\tau}} gives: ##e^{-\frac t {\tau}}##.

Edit. @kuruman beat me to it or I would not have replied!
 
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  • #4
kuruman said:
You have the wrong expression for ##I(t)##. It does not predict that ##I(0) =0.06## A. What is the correct expression to use?

Also, please enter the exponent correctly in LaTeX as e^{-Rt/L} to render as ##e^{-Rt/L}##. Or you could write it as ##\exp(-R t/L)##.
I understand now, thanks. It should have been ##i(t)=0.06e^{-(R/L)t}## since, from time ##t=0## onwards, there isn't a battery connected to the "new" circuit anymore. By setting ##i(t^*)=35\cdot 10^{-3} A## I now get the correct value, thanks.
 
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Related to Help Needed for Solving Electrical Circuit Problem

1. What is an electrical circuit problem?

An electrical circuit problem is a malfunction or issue within an electrical circuit that prevents it from functioning properly. This can include issues such as short circuits, open circuits, faulty components, or incorrect wiring.

2. How can I identify the source of an electrical circuit problem?

To identify the source of an electrical circuit problem, you can use a variety of tools and techniques such as multimeters, circuit testers, and visual inspections. It is important to follow safety precautions and have a basic understanding of electrical circuits before attempting to identify the source of a problem.

3. What are some common solutions for electrical circuit problems?

Some common solutions for electrical circuit problems include replacing faulty components, repairing damaged wiring, and ensuring proper connections. It is important to consult a professional if you are not confident in your ability to solve the problem yourself.

4. How can I prevent electrical circuit problems in the future?

To prevent electrical circuit problems, it is important to regularly inspect and maintain your electrical system. This includes checking for loose connections, replacing old or damaged wiring, and ensuring all components are functioning properly. It is also important to follow safety guidelines and avoid overloading circuits.

5. When should I seek professional help for an electrical circuit problem?

If you are not confident in your ability to safely and effectively solve an electrical circuit problem, it is best to seek professional help. Additionally, if the problem is complex or involves high voltage circuits, it is important to consult a licensed electrician for assistance.

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