The diode used in the circuit shown in fig. has a
 

constant voltage drop at 0.5 V at all current and a  maximum power rating of 100 milli-watts, What should be the value of the resistor R connected in series  with diode and obtaining maximum current

$$\begin{gathered} {\mathrm{V}}_{\mathrm{p}}=0\cdot 5\mathrm{V},\text{ Maximum power rating } \\ \mathrm{P}=100\mathrm{mW}=100\times {10}^{-3}\mathrm{W}\text{ and source voltage } \\ {\mathrm{V}}_{\mathrm{s}}=1\cdot 5\mathrm{V} \\ \mathrm{Now} \mathrm{diode} \mathrm{resistance} \\ {\mathrm{R}}_{\mathrm{D}}=\frac{{\mathrm{V}}_{\mathrm{p}}^2}{\mathrm{P}}=\frac{(0.5{)}^2}{100\times {10}^{-3}}=2.5\mathrm{\Omega } \\ \text{ Current in diode }{\mathrm{I}}_{\mathrm{D}}=\frac{{\mathrm{V}}_{\mathrm{D}}}{{\mathrm{R}}_{\mathrm{D}}}=\frac{0\cdot 5}{2\cdot 5}=0\cdot 2\mathrm{\Omega } \\ \mathrm{Total} \mathrm{resistance} \mathrm{in} \mathrm{the} \mathrm{circuit} \\ {\mathrm{R}}_{\mathrm{T}}=\frac{{\mathrm{V}}_{\mathrm{s}}}{{\mathrm{I}}_{\mathrm{D}}}=\frac{1\cdot 5}{0\cdot 2}=7\cdot 5\mathrm{\Omega } \\ \mathrm{So}, \mathrm{resistance} .\mathrm{R} \mathrm{in} \mathrm{circuit} \\ ={\mathrm{R}}_{\mathrm{T}}-{\mathrm{R}}_{\mathrm{D}}=7\cdot 5-2\cdot 5=5\mathrm{\Omega } \end{gathered}$$