Zener Diode On: Understanding Current Flow in a Circuit

[Pushoam]

Homework Statement

Homework Equations

The Attempt at a Solution

I assume that the zener diode is on.
For this the current flowing through 1k$\Omega ~~i.e. ~~I_1$ should be grater than the 3k$\Omega$ i.e.$I_3$.
$I_3= 10/3~ mA \\I_1 = 4 ~mA$
Clearly,$I_1 > I_3$. So, there is some current going through the zener diode. Hence, the zener diode is on.
Is this correct?

 

[cnh1995]

Your analysis is correct.

 

[Pushoam]

Thank you.

 

[rude man]

You could also see that without the zener the voltage would be 14/(3/4) = 10.5V which is > 10V.

 

[Pushoam]

Thank you.