solving minimum voltage to turn on a diode

Question

Im having issue with this problem. The question asks for the minimum Vs voltage to cause the diode to be on (current flowing through diode). This same question also asks for the current through the diode ID if Vs was 6 volts. The issue Im having is that the answer they give is 122 mA, where as my answer using either .6 or .7 as the voltage drop across the diode comes up too high (around 140 mA). So far this book uses only the ideal diode model and uses usually .6 for the voltage drop. Even when I used 0 volts for the drop across the diode I still came up with a current much higher than theirs. So I have no idea what value they are using for the voltage drop across that diode in order to use it when solving the minimum value for Vs in the second half of the problem!

Answer 1

The book is using 0.7 volts for Vd. Here is a way to solve this circuit.

First off you can simplify by combining the 6 and 12 Ohm resistors.

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Which becomes:

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Then you can use Norton's theorem on the Voltage Source and the 20 Ohm resistor:

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Combine parallel resistors:

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Norton again:

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Now you can write a simple equation:

2V = 6.667i +.7 + 4I