I was doing some physics homework involving direct current circuits and resistors in series, and I started to question the accuracy of the following property of resistors in series, namely that the voltage across the battery is equal to voltage drop across the resistors. But what about the resistance in the wire itself. I wouldn't think that you could just ignore that, especially for very long wires or wires with a significant amount of resistivity. So my question is, why don't text books write
$\Delta V=IR_{1} + IR_{2}+…+IR_{n} + IR_{w}$ where $R_{w}=$ The resistance in the wire
Best Answer
In Nilsson and Riedels textbook: Electric circuits, it is actually stated on page 28 that " when represented in a circuit diagram, copper or aluminum wiring isn't usually modeled as a resistor; the resistance of the wire is so small compared to the resistance of the other elements in the circuit that we can neglect the wiring resistance to simplify the diagram"
Resitors are poorly conducting, while the wiring in circuit diagrams is typically modeled as a perfect conductor (an equipotential), but of course you are correct, and you can calculate the resistance of a wire using Pouillet's Law as long as you have information about the resistivity of the wire. The formula is:
$$R=\rho\frac{\ell}{A}$$ In Introduction to electrodynamics by Griffiths the resistivity of copper at room temperature is given as $1.68*10^{-8}$ Ohm-m. Using this information you can form your own conclusions. (Note that $\rho$ varies with temperature)