Derive equation for voltage across a capacitor

[Fionn00]

Hi I would appreciate some help on this question please.

Derive the basic equation for the voltage across a capacitor as a function of time for a circuit that includes a resistor and capacitor connected in sereis to a battery through a switch.

I know the formulas but haven't the slightest idea how to derive them.


Any help would be great thanks!

 

[berkeman]

Hi I would appreciate some help on this question please.

Derive the basic equation for the voltage across a capacitor as a function of time for a circuit that includes a resistor and capacitor connected in sereis to a battery through a switch.

I know the formulas but haven't the slightest idea how to derive them.


Any help would be great thanks!

Welcome to the PF.

What are you allowed to start with? Can you use the differential equation that relates v(t) and i(t) for a capacitor? Or do you have to start with Maxwell's Equations?

For whichever, you just write the KCL equation for the circuit to start...

 

[Fionn00]

Welcome to the PF.

What are you allowed to start with? Can you use the differential equation that relates v(t) and i(t) for a capacitor? Or do you have to start with Maxwell's Equations?

For whichever, you just write the KCL equation for the circuit to start...

Thanks for the reply.

I'm pretty sure we can use the differential equations.
What KCL equation there are no nodes they are connected in series ?
i1 = 12 ??
All I've got so far is that the moment the switch is closed
i = E/R and the voltage across the capacitor = E - Vr which equals 0 as Vr = E/R*R.

 

[berkeman]

Thanks for the reply.

I'm pretty sure we can use the differential equations.
What KCL equation there are no nodes they are connected in series ?
i1 = 12 ??
All I've got so far is that the moment the switch is closed
i = E/R and the voltage across the capacitor = E - Vr which equals 0 as Vr = E/R*R.

The node for your KCL is the one between the R and the C. Write the sum of currents leaving that node is equal to zero, and use the differential equation that relates i(t) to v(t) for the capacitor part. Just use V = I * R for the resistor part as you suggested.

Then you solve the resulting differential equation, and apply your initial conditions...

 

[Fionn00]

The node for your KCL is the one between the R and the C. Write the sum of currents leaving that node is equal to zero, and use the differential equation that relates i(t) to v(t) for the capacitor part. Just use V = I * R for the resistor part as you suggested.

Then you solve the resulting differential equation, and apply your initial conditions...

What is the differential equation that relates i(t) to v(t) ?

 

[berkeman]

What is the differential equation that relates i(t) to v(t) ?

It should be in your textbook.

If not, go to wikipedia.org and search on capacitor. Then find the section on the current-voltage relation...