ohm
Summary
The ohm (Ω) is the SI unit of electrical resistance, equal to one volt per ampere. In an ohmic conductor, a larger resistance in ohms means less current for the same potential difference, and resistances in series add.
Detail
Meaning: One ohm is the resistance that allows 1 ampere of current when 1 volt is applied across it. Resistance measures how strongly a component opposes charge flow. In base SI units, 1 Ω = 1 kg·m²/(s³·A²). The same unit is used for the resistance of a wire, a resistor, or a whole circuit.
Equation: R = V/I, where R is resistance (Ω), V is potential difference (V), and I is current (A). For a uniform wire, R = ρL/A, where ρ is resistivity (Ω·m), L is length (m), and A is cross-sectional area (m²). Power dissipated is P = I²R, where P is in watts (W).
On the MCAT: Passages give a circuit and ask how current or voltage changes when a resistor is added or removed. Series resistances add: Rs = R₁ + R₂ + ... Parallel resistances combine as 1/Rp = 1/R₁ + 1/R₂ + ..., so Rp is smaller than the smallest branch. Questions also ask how resistance changes if a wire is made longer (R rises) or thicker (R falls). Dimensional analysis may ask you to express the ohm as V/A.
Common confusion: Students mix up resistance with resistivity. Resistance (Ω) depends on the object's shape and its material. Resistivity (Ω·m) is a property of the material alone. Also, R = V/I defines the ohm for any conductor, but constant R (Ohm's law) holds only for ohmic materials.
Sources
- Physics (Giancoli)
- Fundamentals of Physics (Halliday, Resnick, Walker)
- University Physics (Young and Freedman)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.