# Series Circuts

• Jan 30th 2011, 06:18 PM
VonNemo19
Series Circuts
An electromotive force

$\displaystyle E(t)=\left\{\begin{array}{cc}120,&\mbox{ if } 0\leq{t}\leq20\\0, & \mbox{ if } t>20\end{array}\right.$

is applied to an LR series circut in which the inductance is 2o henries and the resistance is 2 ohms. Find the current $\displaystyle i(t)$ is $\displaystyle i(0)=0$.

Now, I would totally know what to do here guys if the voltage wasn't piecewise. How do I proceed?
• Jan 30th 2011, 06:28 PM
dwsmith
Quote:

Originally Posted by VonNemo19
An electromotive force

$\displaystyle E(t)=\left\{\begin{array}{cc}120,&\mbox{ if } 0\leq{t}\leq20\\0, & \mbox{ if } t>20\end{array}\right.$

is applied to an LR series circut in which the inductance is 2o henries and the resistance is 2 ohms. Find the current $\displaystyle i(t)$ is $\displaystyle i(0)=0$.

Now, I would totally know what to do here guys if the voltage wasn't piecewise. How do I proceed?

DE

$\displaystyle \displaystyle L\frac{di}{dt}+Ri=E(t)$

L = 20 and R = 2. For $\displaystyle 0\leq t\leq 20$, then $\displaystyle \displaystyle 20\frac{di}{dt}+2i=120\Rightarrow\frac{di}{dt}+\fr ac{1}{10}i=6$

Solve like a DE

For $\displaystyle t\leq 20$

$\displaystyle \displaystyle 20\frac{di}{dt}+2i=0\Rightarrow\frac{di}{i}=-\frac{dt}{10}$

Solve as a DE.
• Jan 30th 2011, 06:36 PM
VonNemo19
Quote:

Originally Posted by dwsmith
DE

$\displaystyle \displaystyle L\frac{di}{dt}+Ri=E(t)$

L = 20 and R = 2. For $\displaystyle 0\leq t\leq 20$, then $\displaystyle \displaystyle 20\frac{di}{dt}+2i=120\Rightarrow\frac{di}{dt}+\fr ac{1}{10}i=6$

Solve like a DE

For $\displaystyle t\leq 20$

$\displaystyle \displaystyle 20\frac{di}{dt}+2i=0\Rightarrow\frac{di}{i}=-\frac{dt}{10}$

Solve as a DE.

So, I get

$\displaystyle i(t)=\left\{\begin{array}{cc}60(1-e^{-t/10}),&\mbox{ if } 0\leq{t}\leq20\\60(e^2-1)e^{-t/10}, & \mbox{ if } t>20\end{array}\right.$

Right?
• Jan 30th 2011, 06:38 PM
dwsmith
Quote:

Originally Posted by VonNemo19
So, I get

$\displaystyle i(t)=\left\{\begin{array}{cc}60(1-e^{-t/10}),&\mbox{ if } 0\leq{t}\leq20\\60(e^2-1)e^{-t/10}, & \mbox{ if } t>20\end{array}\right.$

Right?

Correct.
• Jan 30th 2011, 06:46 PM
dwsmith
Ok so we have done 25 and 33. Is 35 next? :p
• Jan 30th 2011, 06:49 PM
VonNemo19
Well, dwsmith...Thank you so very much for your help tonight. I think I'll ace this exam that I have Tuesday and I attribute part of my future success to you. I'll ace it because my teacher doesn't even know the material that well - it's obvious in how she responds to some of the tougher questions during class. So, since she doesn't know it that well, she's limited in the types of problems that she can assign because she has to be able not only to grade them, but articulate her reasons in a clear and professional manner as to why she may have marked a particular problem incorrect. Therefore, I think that she will stick to the very basic notions within differential equations and leave a more advanced treatment to someone who knows what they're talking about.

Anyways, thanks again,
VonNemo.
• Jan 30th 2011, 06:55 PM
dwsmith
Quote:

Originally Posted by VonNemo19
Well, dwsmith...Thank you so very much for your help tonight. I think I'll ace this exam that I have Tuesday and I attribute part of my future success to you. I'll ace it because my teacher doesn't even know the material that well - it's obvious in how she responds to some of the tougher questions during class. So, since she doesn't know it that well, she's limited in the types of problems that she can assign because she has to be able not only to grade them, but articulate her reasons in a clear and professional manner as to why she may have marked a particular problem incorrect. Therefore, I think that she will stick to the very basic notions within differential equations and leave a more advanced treatment to someone who knows what they're talking about.

Anyways, thanks again,
VonNemo.

Just be open and honest with her and tell her how you feel. It is a high risk high reward strategy that will 99.9999% backfire i.e. don't try it.