hi 24,
Welcome to AAC.
As this is homework you must post your best attempt at answering, we can the help.
E

 

For Zener diode Vz = 10V
i) vi = 5v < Vz so no flow v0 =0V
ii)vi = 10v which is equal Vz so no flow v0 =0V
vi = 15v > Vz sothere will be flow of current. But I'm unable to calculate how.

this is as much as I know

 

vi = 15v > Vz sothere will be flow of current. But I'm unable to calculate how.

So there is a 15V source and the Zener has 10V across it.
Then how much voltage is across the resistor?

 

So there is a 15V source and the Zener has 10V across it.
Then how much voltage is across the resistor?

15-10 = 5V.

 

There is nothing to do with the 100 Ohm in the circuit since it's parallel to the the Vo

 

15-10 = 5V.

That is correct.

There is nothing to do with the 100 Ohm in the circuit since it's parallel to the the Vo
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I don't understand that as it makes no sense.
Vo is just the voltage across the resistor.
Why do you think the resistor being "parallel to the Vo", whatever that means, is some sort of problem?