Two charged capacitors connected through a resistor

[jh001]

Homework Statement

A 10nF and 20nF capacitor is independently charged to respectively 40V and 50V. The positive sides of the two capacitors are connected, and a 1kΩ resistor is connected across the negative terminals. Find equations for total voltage V_T(t) across the resistor and voltages across each capacitor V₁(t) and V₂(t)

Homework Equations

V(t)=V₀e^-t/RC

The Attempt at a Solution

It seems V_T(0) = 50-40 = 10V.
Can we use V_T(t)=V₂(t)-V₁(t), since the capacitors are connected positive to positive? In that case what value for R do we use for each capacitor?

 

[haruspex]

There may be some law you can appeal to, but it isn't hard to work out from first principles. (I.e., obtain a differential equation for the current.)

 

[jh001]

"work out from first principles" is a bit cryptic/generic and not really helpful. The equation I gave IS in effect a differential equation (well, the solution to one) Can you please elaborate?

 

[haruspex]

"work out from first principles" is a bit cryptic/generic and not really helpful. The equation I gave IS in effect a differential equation (well, the solution to one) Can you please elaborate?

Yes, it's the solution to a differential equation, but you don't know how to apply it because the equation was for a simpler set-up. I'm proposing writing out the differential equation for the set-up in the question and solving that in the same way. You can then be confident in how to apply it here. (It turns out to be just what you might have guessed.)