A capacitor of variable capacitance

[A13235378]

Homework Statement

A capacitor of variable capacitance is being discharged by a resistance R. It is known that the power dissipated by the resistance at any time t is constant and that the initial capacitance is worth Co. Determine the capacitance of the capacitor at time t.

Answer: C (t) = Co - t/R

Relevant Equations

U = RI

Using:

$$i(t)=\frac{U}{R}.e^{-\frac{t}{RC}}

As the power is constant, then the current will be constant, so:

t/RC is constant

I don't know how to proceed anymore. I think you should use some derivative, but I'm still very new to that part, so how can I proceed?

 

[haruspex]

Where does $$i(t)=\frac{U}{R}.e^{-\frac{t}{RC}}$$ come from? If from your notes, you should define the variables and specify the circumstances in which it applies. It seems to contradict your other equation, U=IR.

Yes, the current must be constant, so what is the charge at time t?