What is a zener diode ? Explain how it is used as a voltage Regulator.

Zener diode : A properly doped P-N junction diode which has sharp break down voltage when operated in reverse bias is called "Zener diode"
Symbol :

Zener diode as voltage Regulator :
"The device which gives constant output voltage even if input voltage and load current changes is called voltage regulator".
The circuit diagram for voltage regulator is shown in figure.

By applying $\mathrm{KCL},\mathrm{I}={\mathrm{I}}_{\mathrm{Z}}+{\mathrm{I}}_{\mathrm{L}} \to \left(1\right)$
By applying KVL, ${\mathrm{V}}_{\mathrm{i}}=\mathrm{IR}+{\mathrm{V}}_{\mathrm{z}}$ but ${\mathrm{V}}_{\mathrm{z}}={\mathrm{V}}_0 \to \left(2\right)$
case i) If i/p voltage is constant and load resistance R_L changes 
From (1) $\mathrm{dI}={\mathrm{dI}}_{\mathrm{Z}}+{\mathrm{dI}}_{\mathrm{L}},0={\mathrm{dI}}_{\mathrm{Z}}+{\mathrm{dI}}_{\mathrm{L}}$
${\mathrm{dI}}_{\mathrm{Z}}=-{\mathrm{dI}}_{\mathrm{L}}$
As load resistance (R_L) increases, load current decreases which increases zener current by same amount hence o/p voltage is constant.
case ii) If i/p voltage changes and load resistance constant
from (1) $\mathrm{dI}={\mathrm{dI}}_{\mathrm{Z}}+{\mathrm{dI}}_{\mathrm{L}},\mathrm{dI}={\mathrm{dI}}_{\mathrm{Z}}+0$
$\mathrm{dI}={\mathrm{dI}}_{\mathrm{Z}}$
As the i/p voltage increases, i/p current increases which increases zener current by same amount hence output voltage is constant in this way zener diode can be used as voltage regulator