- #1

arhzz

- 268

- 52

- Homework Statement
- Find the differential equation

- Relevant Equations
- -

Hi,

The following circuit is given, where the switch S is closed at time t=0.

a) Set up the general differential equation (DE) for the current i(t) and bring the result into the following form## \frac{di(t)}{dt} +c_1 i(t)=c_0,## with the constant terms c0 and c1.

Hint: Determine the DE using Kirchoffs laws

b) established ODE.Use here for the exponential approach,i.e. ##i_h(t)=ke^{λt}. ##

(c) Determine the particular solution of the DE

(d)Determine the constant k

(e) Find out the values when i(t) aproaches 0 and infinity, as well as for ## u_L (t) ## Sketch them in a graph

Okay so I'm having problems right at the start. So first I figured that ## i(t) = i_R(t) + i_L(t) ## Using the loop law I get; ## U = u_1 + u_L(t) ## and I can rewrite that as ## i(t)R_1+ L\frac{di_L(t)}{dt} ## now I have rewritten the first equation to look like this; ## i_L(t) = i(t) - u_L(t)(R2+R3)## and now what I have tried is plugging in the first equation in the second one.

$$ U = i(t)R1 + L \frac{d}{dt} (i(t) - u_L(R2+R3) $$ and here is the problem.I get the derivative of di/dt but I'm stuck with this voltage.Usually its a constant term meaning after deriving it simply goes to 0. Now I've tried mixing it up but the same problem persits.I've went ahead and done the rest of the problem,under the assumption that the UL term goes to 0,and the solutions look right ( I get the the right time constant). Can it be that the voltage really goes to 0, if so why? If not what am I doing wrong than?

Thanks for the help!

The following circuit is given, where the switch S is closed at time t=0.

a) Set up the general differential equation (DE) for the current i(t) and bring the result into the following form## \frac{di(t)}{dt} +c_1 i(t)=c_0,## with the constant terms c0 and c1.

Hint: Determine the DE using Kirchoffs laws

b) established ODE.Use here for the exponential approach,i.e. ##i_h(t)=ke^{λt}. ##

(c) Determine the particular solution of the DE

(d)Determine the constant k

(e) Find out the values when i(t) aproaches 0 and infinity, as well as for ## u_L (t) ## Sketch them in a graph

Okay so I'm having problems right at the start. So first I figured that ## i(t) = i_R(t) + i_L(t) ## Using the loop law I get; ## U = u_1 + u_L(t) ## and I can rewrite that as ## i(t)R_1+ L\frac{di_L(t)}{dt} ## now I have rewritten the first equation to look like this; ## i_L(t) = i(t) - u_L(t)(R2+R3)## and now what I have tried is plugging in the first equation in the second one.

$$ U = i(t)R1 + L \frac{d}{dt} (i(t) - u_L(R2+R3) $$ and here is the problem.I get the derivative of di/dt but I'm stuck with this voltage.Usually its a constant term meaning after deriving it simply goes to 0. Now I've tried mixing it up but the same problem persits.I've went ahead and done the rest of the problem,under the assumption that the UL term goes to 0,and the solutions look right ( I get the the right time constant). Can it be that the voltage really goes to 0, if so why? If not what am I doing wrong than?

Thanks for the help!

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