Resistance and Conductors flashcards

$R=\frac{\rho L}{A}$: resistance ($\Omega$) equals resistivity $\rho$ ($\Omega \cdot \text{m}$) times length L (m) divided by cross-sectional area A (${\text{m}}^2$). R rises with length and falls as area grows.

Resistivity ($\rho$, in $\Omega \cdot \text{m}$) is a property of the material alone. Resistance (R, in ohms) belongs to a specific object and also depends on its length and cross-sectional area.

Area depends on diameter squared ($A=\frac{\pi d^2}{4}$), so area drops to 1/4 and resistance becomes 4 times larger, not 2 times. Always square the diameter ratio.

Metals gain resistance when heated (copper about 0.4 percent per °C) because electrons scatter more. Semiconductors, carbon and NTC thermistors lose resistance as they warm (negative coefficient).

It depends on what is fixed. At the same voltage, $P=\frac{V^2}{R}$, so the smaller R dissipates more. At the same current, $P=I^{2}R$, so the larger R dissipates more.

Only on a de-energized circuit, with the part isolated (at least one lead disconnected), since the meter supplies its own current. Parallel paths, including your fingers on both probes, make the reading too low.

Thicker. A larger gauge number means a thinner wire, so 12 AWG has less resistance per foot and can carry more current than 14 AWG.

Open: a break in the path with effectively infinite resistance, so no current flows (the source voltage can appear across the gap). Short: an unintended very low-resistance path bypassing the load, causing very large current and heat.