A diode, a resistor, and a battery are connected in a

Chapter 43, Problem 48

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A diode, a resistor, and a battery are connected in a series circuit. The diode is at a temperature for which kBT 5 25.0 meV, and the saturation value of the current is I0 5 1.00 mA. The resistance of the resistor is R 5 745 V, and the battery maintains a constant potential difference of e 5 2.42 V between its terminals. (a) Use Kirchhoffs loop rule to show that e 2 DV 5 I 0R 1ee DV/k BT 2 12 where DV is the voltage across the diode. (b) To solve this transcendental equation for the voltage DV, graph the left-hand side of the above equation and the righthand side as functions of DV and find the value of DV 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 DV/I, at the voltage in part (b). (e) Find the dynamic resistance of the diode, which is defined as the derivative d(DV)/dI, at the voltage in part (b).