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schematic

simulate this circuit – Schematic created using CircuitLab

In the circuit shown if current is flowing from negative side of battery to positive side how multimeter can know the existence of resistor before electrons in wire hits the resistor?

I mean how multimeter measures current before it reaches the resistor? How it knows that a resistor exists?

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The meter is only measuring the amount of charge per unit time that is passing through its internal shunt resistance. It doesn't know or care that there is a resistor in the way.

Your resistor is just limiting the current (charge/second) that the voltage source can "push" through the meter. Think of a water meter measuring water flow. If you put a kink in the hose upstream, the water flow slows down and the meter measures less flow.

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