How To Calculate Total Resistance

Total resistance, also called equivalent resistance, is the value of a single resistor that would draw the same current from the same supply as the whole network. Replace the network with that one resistor and nothing else in the circuit changes.

Series connection means the components sit end to end on one path. The current has no choice but to flow through every resistor, and each one drops part of the voltage. Because the voltage drops add up to the supply voltage, the resistances themselves add up.

Series has a useful consequence: the largest resistor always drops the largest share of the voltage. Two resistors of 100 and 300 ohms across 12 volts split it into 3 volts and 9 volts, in proportion to their values.

Parallel connection means every resistor sits across the same two nodes. Each one sees the full supply voltage, and the currents add. Because conductance adds rather than resistance, the reciprocals of the resistances are what sum.

The parallel rule always produces a total smaller than the smallest branch. Three resistors of 100, 200 and 300 ohms give 54.5455 ohms, which is below the 100 ohm minimum. If your answer is larger than the smallest resistor, you have added instead of combining reciprocals.

Two resistors in parallel have a shortcut worth memorising: the product over the sum. Two 100 ohm resistors give 100 times 100 divided by 200, which is 50 ohms. The shortcut does not extend cleanly to three or more, so use reciprocals there.

Identical resistors in parallel divide evenly. Three 300 ohm resistors in parallel give 100 ohms, and n identical resistors give R divided by n. This is a fast sanity check before doing any arithmetic.

Conductance is the inverse of resistance and is measured in siemens. Adding conductances in parallel is why reciprocals appear in the formula, and thinking in conductance makes the rule feel natural rather than arbitrary.

Real circuits mix both. The usual method is to collapse the obvious parallel groups first, redraw the circuit with those replaced by their equivalent, and repeat until a single value remains. Order matters only for convenience, never for the answer.

A common trap is a resistor that looks parallel but is not. If another component sits between the two ends of the resistors, they are not across the same nodes and the parallel rule does not apply.

Tolerance matters in practice. A one percent resistor is close to its marked value, but combining tolerances means the total can drift by more than any single part, especially in parallel where small branches carry large currents.

Power rating is separate from resistance. Splitting a load across parallel resistors shares the heat, which is why parallel banks are used when a single resistor would overheat even though the equivalent resistance is small.