Under the assumption that the voltage is [itex]V_f\left(1-e^{-\frac{t}{RC}}\right)[/itex], where [itex]V_f[/itex] is the final voltage, how would I determine the relationship between current [itex]I[/itex] and time [itex]t[/itex]?(adsbygoogle = window.adsbygoogle || []).push({});

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

[itex]L[/itex] the magnetic inductance, [itex]R[/itex] the resistance, and [itex]C[/itex] the capacitance, are constants.

How would I plot current [itex]I[/itex] as a function of time [itex]t[/itex]? (The only variables here are [itex]I[/itex] and [itex]t[/itex].) Let's assume initial conditions of [itex]I=0[/itex] and [itex]t=0[/itex]. 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!

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

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