Does current flow through or across a resistor?

Current flows across a resistor.

Explanation:

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It's not exactly clear what you think the difference is between "through" and "across".

A resistor has two wires.  Electric current that flows into one wire, continues through the entire body of the resistor and out through the other wire.  If there's a crack or break anywhere along the body of the resistor, the circuit will be 'open' and the current will stop flowing.

Now, if you were to connect a voltmeter between the ends of the resistor, the meter would measure and indicate the difference in electric potential between those two points.  That would be called the voltage 'across' the resistor.  Numerically, it would be equal to the product of the resistor's resistance and the current through it.  

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