anonymous
  • anonymous
please help. medal and fan
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Consider a series circuit consisting of a resistor of R ohms, an inductor of L henries, and variable voltage source of V(t) volts (time t in seconds). The current through the circuit I(t) (in amperes) satisfies the differential equation: dI/dt + (R/L)I = (1/L)V(t) Find the solution to this equation with the initial condition I(0)=0, assuming that R=50Ω, L=5 H, and V(t) is constant with V(t)=10 V.
anonymous
  • anonymous
I'm having trouble differentiating it
anonymous
  • anonymous
I(e^(RT/L)) = integral: (V(t)e^(RT/L))/L

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anonymous
  • anonymous
with the numbers plugged in Ie^(10t) = integral: (V(t)e^(10t))/5
anonymous
  • anonymous
That's as far as I got
anonymous
  • anonymous
maybe treat V(t) as a constant?
anonymous
  • anonymous
@rational
anonymous
  • anonymous
I also plugged in 10 for V(t) and got -1/5 for C when I(0)=0.
sparrow2
  • sparrow2
i(r/L) this is constant,isn't it?
anonymous
  • anonymous
What do you mean?
sparrow2
  • sparrow2
because r/L is constant becasue r and L are constants
sparrow2
  • sparrow2
or i'm missing smth
anonymous
  • anonymous
ya when i plugged those values in I got e^10T
sparrow2
  • sparrow2
v(t) is also constant it's 10
anonymous
  • anonymous
yep, but the question is asking me to find an equation for V(t)
sparrow2
  • sparrow2
v(t)=10 this is equation
anonymous
  • anonymous
I wish it was, I already tried that lol
sparrow2
  • sparrow2
when it is writte above v(t)=10v v here is volt not a variable i guess
anonymous
  • anonymous
i think it is a constant but i'm not sure where i need to apply it
anonymous
  • anonymous
The only other part of the question is V(t) =
anonymous
  • anonymous
@triciaal
triciaal
  • triciaal
don't have the solution, my input: dl/dt = dl/dv*dv/dt for some reason I would be separating the variables and integrating when you integrate you add the constant here the constant is given as 10V
triciaal
  • triciaal
|dw:1433057995387:dw|
amoodarya
  • amoodarya
\[\frac{ di }{dt }+\frac{ r }{ l }i=\frac{ 1 }{ l}v(t)\\r=50\\l=5\\v(t)=10\\\frac{ di }{dt }+\frac{ 50 }{ 5 }i=\frac{ 1 }{ 5}10\\\] and now solve this differential equation \[\frac{ di }{dt }+10i=2\\ \rightarrow * e^{10t} \\e^{10t} (\frac{di}{dt}+10i)=2e^{10t}\\e^{10t} di +e^{10t} 10i dt =2e^{10t}dt\\now\\ \space \\\ d(e^{10t}i)=2e^{10t}dt \] now apply integral \[\int\limits_{0}^{t}d(e^{10t}i)=\int\limits_{0}^{t}2e^{10s}ds \\e^{10t}i(t)-e^0i(0)=2e^{10t}-2\] and now apply I(0)=0 so you have \[e^{10t}i(t)-0=2(e^{10t}-1)\\ \rightarrow * e^{-10t} \\i(t)=2(1-e^{-10t})\]
anonymous
  • anonymous
@amoodarya I tried that but it was wrong. The question is asking for V(t) and i'm not sure what they want
amoodarya
  • amoodarya
v(t) is voltage of ? resistant or self ?
anonymous
  • anonymous
yesh veryish goosh sir

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