One path stacks, extra doors help
Series is a queue: one path, so every ohm stacks: , and the total always lands ABOVE either resistor. The subscripts are just name tags: and are the two resistors' own values in ohms, and — t for total — is the single resistance that could stand in for the pair, which is what you are solving for. Parallel is extra doors: every new branch makes the flow easier, so the total drops BELOW even the smallest branch — always. The relation is product over sum: (read aloud: R-total equals R-one R-two over R-one plus R-two).
Two nuggets worth owning: two EQUAL branches halve, , no arithmetic — and the instinct check comes free before any computing: series above both, parallel below both. An answer on the wrong side of that line is wrong before the units even get a word in.
- = Total resistance
- = Resistance 1
- = Resistance 2
each variable a resistance
- = Total resistance
- = Resistance 1
- = Resistance 2
each variable a resistance
- = Voltage (voltage)
- = Current (electric current)
- = Resistance (resistance)