parallel resistors

Meaning: Resistors are in parallel when both ends of each connect to the same two nodes, giving the current separate branches. Every branch has the same potential difference, equal to the source voltage. By I = V/R, more current flows through the smaller resistance. The branch currents add to the total current (Kirchhoff's junction rule). Each added branch is another path for charge, so the equivalent resistance falls.

Equation: 1/Req = 1/R₁ + 1/R₂ + 1/R₃ + … where Req is the equivalent resistance and R₁, R₂, R₃ are the branch resistances, all in ohms (Ω). For two resistors, Req = R₁R₂/(R₁ + R₂). For n identical resistors, Req = R/n.

On the MCAT: Expect a battery with several branches and a request for Req, the total current, or the current or power in one branch. A common prediction: adding a resistor in parallel lowers Req and raises the total current, while the existing branches are unchanged for an ideal battery because their voltage is unchanged. Since P = V²/R, the smallest resistor dissipates the most power in a parallel set.

Common confusion: Students add the resistances directly (the series rule) or forget to invert after summing the reciprocals. Check the answer: Req must be less than the smallest branch resistance. Also, voltage, not current, is the same in every branch.