Hi, our professor gave us a homework here is the description:

We must prove if RL and RC circuits acts as integrator or differentiator or both using differential equations. I know differential equations but sadly i am very bad at circuits and terrible at solving RL,RC circuits using dif. eq. . So far i got help from some of my friends and internet and already solved RC as differentiator but if its wrong please correct my mistakes andon RC as integrator is halfway done.

Here is my progression:

*******

The current through the circuit is the same as the current through the capacitor then:

iC=C*(dVi/dt)

So the voltage across the resistor is

VR=R*iC=R*C*(dVi/dt)

As we measure the output voltage across the resistor then the output voltage is

Vo=R*C*(dVi/dt)

Thus the RC circuit with an output across the resistor is a differentiator since it differentiates the input voltage.

This one is one of the solutions with the help i get but on this video on youtube

solution is different than mine which one is true ? Did i made mistake ?

********

I still stuck at RL as integrator and differentiator. So if you can Show me some way to do it or solve RL as integrator or diffferentaitor to Show me how to do other i would really appericiate it.

Btw we got 1 week and i have 5 days left so this homework is kinda urgent and sorry for my English.

We must prove if RL and RC circuits acts as integrator or differentiator or both using differential equations. I know differential equations but sadly i am very bad at circuits and terrible at solving RL,RC circuits using dif. eq. . So far i got help from some of my friends and internet and already solved RC as differentiator but if its wrong please correct my mistakes andon RC as integrator is halfway done.

Here is my progression:

*******

The current through the circuit is the same as the current through the capacitor then:

iC=C*(dVi/dt)

So the voltage across the resistor is

VR=R*iC=R*C*(dVi/dt)

As we measure the output voltage across the resistor then the output voltage is

Vo=R*C*(dVi/dt)

Thus the RC circuit with an output across the resistor is a differentiator since it differentiates the input voltage.

This one is one of the solutions with the help i get but on this video on youtube

********

I still stuck at RL as integrator and differentiator. So if you can Show me some way to do it or solve RL as integrator or diffferentaitor to Show me how to do other i would really appericiate it.

Btw we got 1 week and i have 5 days left so this homework is kinda urgent and sorry for my English.

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