FQRMULA SHEET when Rin tends infinity. V & 0 & Semiconductor Diode Electrica) conductivity material [Carrier density per unit volume (n) electronic charge (...

A diode, a resistor, and a battery are connected in a series circuit. The diode is at a temperature for which $k_{\mathrm{B}} T=25.0 \mathrm{meV},$ and the saturation value of the current is $I_{0}=1.00 \mu \mathrm{A} .$ The resistance of the resistor is $R=745 \Omega$ and the battery maintains a constant potential difference of $\varepsilon=2.42 \mathrm{V}$ between its terminals. (a) Use Kirchhoff's loop rule to show that
$$\boldsymbol{\varepsilon}-\Delta V=I_{0} R\left(e^{e \Delta V / k_{\mathrm{B}} T}-1\right)$$
where $\Delta V$ is the voltage across the diode. (b) To solve this transcendental equation for the voltage $\Delta V,$ graph the left-hand side of the above equation and the right-hand side as functions of $\Delta V$ and find the value of $\Delta V$ at which the curves cross. (c) Find the current $I$ in the circuit. (d) Find the ohmic resistance of the diode, defined as the ratio $\Delta V / I,$ at the voltage in part (b). (e) Find the dynamic resistance of the diode, which is defined as the derivative $d(\Delta V) / d I$ , at the voltage in part (b).