The barrier potential of a $p-n$ junction depends on:
$(1)$ Type of semiconductor material
$(2)$ Amount of doping
$(3)$ Temperature
Which one of the following is correct?

The voltage-current characteristic of a diode during forward bias is given by $I = 7.8 \times 10^{-5} e^{6.5 V_D}$,where $I$ is the current in $mA$ and $V_D$ is the diode voltage in $V$. Find the dynamic resistance of the diode in $\Omega$,when the current is $4 \ mA$.

$A$ $2 \text{ V}$ battery is connected to a diode in forward bias. $A$ voltage of $0.5 \text{ V}$ is dropped across the diode,which is independent of the current flowing through it. $A$ current greater than $10 \text{ mA}$ causes excessive heating and damages the diode. If a current of $5 \text{ mA}$ is required in the diode,what value of series resistance must be connected in the circuit?

In a $P-N$ junction diode,if the $P$ region is more heavily doped than the $n$ region,then the depletion layer is:

The example for non-ohmic resistance is

For a $pn$ junction,the width of the space charge region (depletion layer) is approximately $\qquad$ $\mu m$.