Zener Diode Circuits Volts

How to find the permissible range of E in a zener diode.?

Need help on a homework question:

With the same zener diode 1N4735A in the circuit, but with R1 = 330Ω and
RL = 1.5kΩ, what will be the permissible range of E? In other words what will be
Emin and Emax? Use an ideal model for diode and note IZK = 1mA and IZM = 146mA
for the diode.

The circuit in question can be found here: http://www.freeimagehosting.net/image.php?f62bfa235f.png
Also the zener voltage of a 1N4735A is nominally 6.2 Volts.

take a thevenin equivalent of everything but the zener
Vth = 12v * 1500/(1500+330)
Vth = 9.84V

Rth = 1500*330/(1500+330)
Rth = 270.5 ohms

1 ma through 270 ohms will drop 270 mv

Therefore Vz max = 9.84-0.274
Vz max = 9.56V

146 ma through 270 ohm will drop 39.42V
Only 9.84 V is available so Izmax cannot be reached regardless of zener voltage

therefore any zener below 9.56V is ok

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