Capacitance for a parallel RC circuit

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Homework Statement

A circuit consists of a Zener diode, capacitor and resistor in parallel. Voltage to be maintained across the components is 4.7V, power 5mW. Find the values for resistor and capacitor

Homework Equations

(Below)

The Attempt at a Solution

I found the resistance by taking P=V^2/R, and using the given values for P and V, R=4.4k(Ohms). I have a problem with finding the capacitance value.
I found the current for the resistor. But there're 2 unknowns now, the capacitor value and the Ic. I've come up to the point where two equations are obtained: Ic=CdV/dt; Ir=V/R. How do I proceed from here to get C? Is this the correct way of approaching this?

Thanks.

 

[CEL]

The problem is incomplete. Is this circuit connected to the output of a rectifier? If so, is it full wave or half wave? What is the peak voltage of the rectified voltage. (I assume the frequency is 60 Hz).