An example of a circuit
This circuit has a diode in it which acts as a resistor with resistance R1=10 ohms
if the current through it is positive and R2=10000 ohms otherwise. The voltage
is E(t)=110*cos(w*t) where w=2*PI*60. From Kirchoff's laws we obtain:
I1 + I2 + I3 = 0
L*dI1/dt  RD*I2 = E(t)
Q/C + RD*I2 + R * I3 = 0
dQ/dt = I3
RD = R1 if I2>0 and R2 if I2 < 0
Thus
I2 = I1  I3 = I1  dQ/dt
and we can eliminate I2 from the second and third equation:
L*dI1/dt  RD*(I1  dQ/dt) = E(t)
Q/C + RD * (I1  dQ/dt) + R * (dQ/dt) = 0
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Instructions on using the Applet
Marek Rychlik (rychlik@u.arizona.edu)
Author's Home Page: http://alamos.math.arizona.edu
