protectionzener
I want to select x as resistance for the protecting resistor (upper).
The zener diode can hold up to 4A
If I was guaranteed to have current through zener lower than 4A, I could consider its voltage to be 5.1V and the voltage through load to be 5.1 V.
But I'm not. So, I can't consider the voltage to be 5.1 V and I can't calculate a voltage drop for protecting resistor in terms of x, because I don't know the current in curcuit because I don't know the resistance of zener.
Rather than going to 'no resistor' consider what happens if we just use resistors of different (lower) values and look at the pattern. As we reduce the resistor value the current through the zener will rise. Even if the voltage source is not perfect the power dissipated by the zener will cause it to fail due to overheating.
The zener diode you reference has a zener-voltage of 5.1V and a power rating of 1W. You want to place a resistor in series with the 9V source and the zener diode to limit current draw.
The datasheet for the IN4733 states that at a zener current of 49mA the zener voltage is at the rated 5.1V. The only calculation you need to do is to size the resistor such that you have at least 49mA, although lower current would also likely give you around the 5.1V zener rating. Normally you would look at the datasheet for a chart to give you this information, but the one I found left this information out.
$$ R = \frac{9-5.1}{10mA} = 390 \Omega$$
But, again, larger sized resistors are likely to give you the voltage you want with lower power dissipation. Test to verify.
Best Answer
To find the limits of the resistor needed x, proceed as follows :
1) For zener to just turn on, Voltage across the load resistance ( 2400 ohms in your case) must be greater than or equal to the zener voltage.
Applying Voltage divider rule ;
Vi = Input Voltage
Vz = Zener Voltage
From here, you get the maximum resistance x needed.
2) For Zener to be in its working limits, proceed as follows :
Current through the zener will be max ( Say Izmax). So
Ix is current through x
IL is current through Load resistance, which equals [ Vz/ RL ].
From here, you compute the current through x.
Since Ix = [ Vi - Vz ] / x ; you get the second limit for your resistance.