equivalent resistance

Meaning: Equivalent resistance, Req, is the single resistance that could replace a network of resistors and draw the same current from the same source. Series resistors share one current and their voltage drops add, so resistances add. Parallel resistors share one voltage and their currents add, so the reciprocals add. A new parallel path gives current another route, so Req falls.

Equation: Series: Req = R₁ + R₂ + R₃. Parallel: 1/Req = 1/R₁ + 1/R₂ + 1/R₃. Req and each R are in ohms (Ω). Total current: I = V/Req, with V in volts and I in amperes.

On the MCAT: A passage gives a mixed circuit. Collapse each parallel group, add the series parts, find I = V/Req, then work back to the current or voltage at one resistor. Questions ask what happens to Req, total current or power when a resistor is added or a switch opens. n equal resistors R in parallel give R/n.

Common confusion: Adding a resistor does not always raise Req. In series it does; in parallel it lowers Req, even if the new resistor is very large. Parallel Req is smaller than the smallest branch.