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Consider the circuit diagram below-

enter image description here

Two batteries of different voltages are placed in parallel, however as I was told that KVL is applicable to all loops if there is no varying magnetic fields, applying KVL to that loop yields (going in the clockwise direction) -$$-E_2+E_1=0 \\ \implies -6V+12V=0 \\ \implies 12V=6V$$ Which is absurd. I searched for the answer quite a while and found some similar question where an answer explicitly address this condition. But I want to know why I can't apply the KVL here when it is applicable for all loop?

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    $\begingroup$ You're neglecting the voltage drop over the resistors. $\endgroup$
    – DanDan面
    Commented Dec 4, 2021 at 20:49
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    $\begingroup$ What about the potential differences across the resistors? $\endgroup$
    – Farcher
    Commented Dec 4, 2021 at 20:49
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    $\begingroup$ You can apply KVL, but you didn't. $\endgroup$
    – Bob D
    Commented Dec 4, 2021 at 21:18

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