In the given circuit,the current is $0.1 \ A$. The resistance of the $P-N$ junction is .... $\Omega$.

In the given circuit,the voltage across the $P-N$ junction diode remains constant at $0.5 \ V$ regardless of the current. The maximum power rating of the diode is $100 \ mW$. What should be the value of $R$ in $\Omega$ to obtain the maximum current in the circuit?

In an unbiased $p-n$ junction:

In a $PN$-junction diode,the reverse saturation current is ${10^{-5}} \ A$ at $27^\circ C$. Calculate the forward current for a voltage of $0.2 \ V$. Given: $[\exp(7.62) = 2038.6, \ k_B = 1.4 \times {10^{-23}} \ J/K, \ e = 1.6 \times {10^{-19}} \ C]$.

The diode used in the circuit shown in the figure has a constant voltage drop of $0.5\; V$ at all currents and a maximum power rating of $100\; mW$. What should be the value of the resistor $R$,connected in series with the diode,to obtain the maximum current? (in $\Omega$)

Statement $I :$ When a $Si$ sample is doped with Boron,it becomes $P$-type and when doped by Arsenic it becomes $N$-type semiconductor such that $P$-type has excess holes and $N$-type has excess electrons.
Statement $II$ : When such $P$-type and $N$-type semiconductors are fused to make a junction,a current will automatically flow which can be detected with an externally connected ammeter.
In the light of above statements,choose the most appropriate answer from the options given below.