Question

if the depletion capacitance of pn junction diode is cd at equilibrium and the built in potential is 0.5v how much reverse voltage has to be applied to reduce the depletion capacitance to 0.5cd

Answer 1

The charge at equilibrium state:

$$Q=C_dV=0.5C_d.$$

And it remains the same. The new depletion capacitance of $0.5C_d$ should be achieved at new voltage:

$$V_n=\frac{Q}{C_{dn}},$$

substitution of the previously determined charge gives

$$V_n=\frac{0.5C_d}{0.5C_d}=1\text{ V}.$$