I've run into a slight confusion, which I'm hoping someone can clear up for me. We have a book that states resistors are used to limit current flowing through a load. However, Kirchhoff's 1st Law states that the amount of current flowing into a node must equal the current flowing out of it, i.e. the current remains constant throughout the circuit. I understood this to mean that it's the voltage that drops, not the current, but this book states that the resistor can be used to limit the current as well as the voltage.

Voltage across a resistor and current through a resistor are always proportional to each other (V=I*R, or I=V/R). That's Ohm's Law.

If you apply a fixed voltage V to a resistor, this will result in a current (in the amount of I=V/R) flowing through the resistor. In this case the resistor determines (or "limits") the current drawn from the voltage source

^{1)}. OTOH, if you feed a fixed amount of current through a resistor, this will result in a voltage drop (in the amount of V=I*R) across the resistor. There can't be a current flowing though a resistor w/o voltage across the resitor (and vice versa).

Things are getting more complicated, though, when neither a

*constant* voltage nor a

*constant* current is apllied to the resistor, but when the resistor of interest is part of a complex circuit, where other components in the circuit also influence the voltage across the resistor and/or the current through the resistor. V=I*R still applies, but neither V nor I is a priori known then. Then you need to analyze the whole circuit

^{2)} in order to find either the current through the resistor, or the voltage across the resistor. Once the current through the resistor is known, the voltage across the resistor can be easily calulated as V=I*R, or vice versa, once the voltage across the resistor is known, the current through the resistor can be easily calculated as I=V/R.

And yes, the same amount of current which flows into the first pin of the resistor, also flows out from the second pin of the resistor, or in other words, the current flows

*through* the resistor.

^{1)} The term "

*limits* the current" is usually used when the resistor is connected in series with another component, when this other component would draw a large amount of current when connected alone to the same voltage source. Due to the series resistor, the current though the component (and through the resistor) gets limited then.

^{2)} That's where Kirchoff's Laws come into the play as well. Based On Ohm's and Kirchoff's Laws you'll setup N equations with N unknowns for the circuit, and solve for various currents and voltages in the circuilt.