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When Vi<-2V, the D1 & D2 both will be turned on and both of them will be considered as short circuits. But how do I find the output voltage with two batteries connected in parallel like this? I've read the answers to this question here -> https://physics.stackexchange.com/q/64509/ that we shouldn't connect two batteries in parallel.

I've also asked on Physics SE and someone said my assumption about the two diodes can be turned on at the same time is wrong. D1 will be turned on when the input voltage is less than 5V, and D2 will be turned on when the input voltage is less than -2V. Therefore, when the input voltage is less than -2V, it satisfies both D1 and D2, right?

Can someone explain to me why is my assumption about that is wrong?

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    \$\begingroup\$ The two batteries are not connected in parallel. If they were electrically parallel then they would have the same voltage across them, which is impossible. \$\endgroup\$ Commented Sep 25, 2021 at 12:53

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It may depend on whether you assume they are theoretical batteries and theoretical diodes, or real batteries and real diodes.

If they are theoretical, then the 5V battery and D1 will not allow Vo to drop below 5V under any circumstances.

If Vo is never below 5V, then the 2V battery will never do anything, as D2 will be reverse-biased.

If you set Vi negative, then it just causes a current to flow between the 5V battery and Vi, through D1 and the 1k resistor.

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You are assuming that if the input voltage is less than -2 V that the output voltage must also be less than -2 V. That's an invalid assumption. Current flowing through the resistor may cause the output voltage to be different from the input voltage.

Since this looks like homework I am only giving you that hint.

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