Can an integral that is a variable of itself be solved?

[kmarinas86]

Under the assumption that the voltage is V_f\left(1-e^{-\frac{t}{RC}}\right), where V_f is the final voltage, how would I determine the relationship between current I and time t?

I = \int_0^T \frac{V_f\left(1-e^{-\frac{t}{RC}}\right) - RI}{L} \,dt \,

L the magnetic inductance, R the resistance, and C the capacitance, are constants.

How would I plot current I as a function of time t? (The only variables here are I and t.) Let's assume initial conditions of I=0 and t=0. My problem here is that the variable I am trying to calculate is a variable inside the integral that is used in deriving the variable itself! How are such problems handled? Any help is appreciated!

 

[felper]

Read about this

http://en.wikipedia.org/wiki/Integral_equation

 

[SammyS]

So, I take it that you mean that \displaystyle I(T\,) = \int_0^T \frac{V_f\left(1-e^{-\frac{t}{RC}}\right) - RI(t)}{L} \,dt\,.

Differentiate both sides w.r.t T and solve for I'(T). See if you can integrate the result to get I(τ).

 

[Simon Bridge]

OP has a related question in this other post.

note:
I=\int RI.dt - differentiate both sides gives

dI/I = R.dt

... what was the problem?