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Does it mean that we can't make an equivalent circuit using the Thevenin Theorem? My question specifically is when using theoretical circumstances on this image. Theoretically speaking the Vth = Vab = 0. What happens then? enter image description here

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    \$\begingroup\$ this is actually a very important example : a lot of measurement techniques involve this condition, called a "bridge" or "Wheatstone bridge" which is currently "balanced" - for example, measuring the resistances in a strain gauge. What you found is an important characteristic : the measurement is independent of the voltage source V3 (so battery state doesn't introduce measurement errors) \$\endgroup\$
    – user16324
    Jan 3, 2022 at 14:38

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Does it mean that we can't make an equivalent circuit using the Thevenin Theorem?

No, you can make an equivalent circuit but, the voltage source will be 0 volts. The equivalent circuit will be just a resistor (450 Ω by my calculation) connected to 0 volts.

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