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# 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`

View Instructions on using the Applet

Marek Rychlik (rychlik@u.arizona.edu)