A capacitor of variable capacitance

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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?
 

Answers and Replies

  • #2
haruspex
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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?
 

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