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The resistor values are the same so they split the 30V that is across both of them.how do you get the -5v in the middle in your first diagram?
The diode voltage is non-linear only when its temperature or current changes. Both do not change so the circuit is linear and Ohm's Law can be used.we can not use ohms law...because the circuit is non linear. And ohms law is only applicable to linear circuits.
Your 2nd diagram is COMPLETELY WRONG!
Without the diode:
The 10k resistor on the right side has 15V across it and the right battery is -20V so the middle junction where the diode will be is -20V minus 15V= -5V.
The 10k resistor on the left side has 15V across it and the left battery is +10V so the middle junction where the diode will be is +10V minus 15V= -5V.
"taking away" means subtracting right? if we take away 15 from -20 we should have -20-15=-35?