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Has the saying" voltage of battery is equal to voltage of resistor" got something to do with the fact that ideal circuits are thought to have no resistance? Is it just a way of saying that since the whole circuit doesn't have much resistance, it's better to say the resistor alone can be considered as the circuit?

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    $\begingroup$ Wires generally have low resistances compared with regular resistors. Not in all applications, but mostly… $\endgroup$
    – Jon Custer
    Commented Nov 24, 2022 at 22:36

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Yes. That's why if you need to measure the voltage across a resistor accurately, you use the Kelvin connection.

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