Applications - A Guide to MATLAB for Beginners and Experienced Users - page 209

i

R

resistor

V 0

diode

battery

FigureC-1: ANonlinearElectricalCircuit

hour with the quarterback. The corresponding numbers for the runners,
receivers and linemen are 0.4, 0.3, and 0.6, respectively.
(a) How many hours should Nerv spend with each group?
(b) Suppose he only needs 15 points to win; then how many?
(c) Finally suppose, despite needing only 15 points, that the troops are
getting restless and he can only dish out 70 criticisms this week. Is
Nerv getting the most out of his week?
10. This problem, suggested to us by our colleague Tom Antonsen, concerns
an electrical circuit, one of whose components does not behave linearly.
Consider the circuit in Figure C-1.
Unlike the resistor, the diode is a nonlinear element — it does not obey
Ohm's Law. In fact its behavior is specified by the formula

i = I 0 exp( V D / V T ) , (1)

where i is the current in the diode (which is the same as in the resistor by
Kirchhoff's Current Law), V D is the voltage across the diode, I 0 is the leak-
age current of the diode, and V T = kT / e , where k is Boltzmann's constant,
T is the temperature of the diode, and e is the electrical charge.
By Ohm's Law applied to the resistor, we also know that V R = iR ,
where V R is the voltage across the resistor and R is its resistance. But by
Kirchhoff's Voltage Law, we also have V R = V 0 − V D . This gives a second