resistance
Summary
Resistance (R) is a measure of how strongly a conductor or circuit element opposes the flow of charge, in ohms (Ω). For an ohmic element V = IR, and R = ρL/A, so resistance rises with length and falls with cross-sectional area. Parallel resistors lower the total.
Detail
Meaning: Resistance measures how much a component opposes current. Moving charges collide with the atoms of the material and lose energy as heat. At a given voltage, a larger R gives a smaller current. R depends on the material (resistivity ρ), the length, and the cross-sectional area. Resistors in series add: Rs = R1 + R2 + ... Resistors in parallel combine as 1/Rp = 1/R1 + 1/R2 + ... Power dissipated is P = I²R. In fluids, the analogous resistance to flow rises steeply as vessel radius falls (proportional to 1/r⁴).
Equation: V = IR and R = ρL/A, where V is potential difference (volts, V), I is current (amperes, A), R is resistance (ohms, Ω = V/A), ρ is resistivity (Ω·m), L is length (m), and A is cross-sectional area (m²).
On the MCAT: A passage gives a circuit diagram. You find the equivalent resistance, then the current from V = IR, then the power or the voltage drop across one resistor. Other questions ask how R changes when a wire is stretched, thickened, or replaced by another material, or what happens to total current when a resistor is added in series or in parallel.
Common confusion: Students often add parallel resistors directly. The equivalent resistance of a parallel set is smaller than the smallest branch, because each branch gives the current another path. Also, resistance is a property of the object (its material and shape), not of the current or voltage applied.
Sources
- Physics (Giancoli)
- Fundamentals of Physics (Halliday, Resnick, Walker)
- College Physics (Serway and Vuille)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.