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Lesson 35 · Series and parallel
One path stacks, extra doors help
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One path stacks, extra doors help

Series is a queue: one path, so every ohm stacks: Rt=R1+R2R_t = R_1 + R_2, and the total always lands ABOVE either resistor. The subscripts are just name tags: R1R_1 and R2R_2 are the two resistors' own values in ohms, and RtR_t — 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: Rt=R1R2R1+R2R_t = \dfrac{R_1 R_2}{R_1 + R_2} (read aloud: R-total equals R-one R-two over R-one plus R-two).

Two nuggets worth owning: two EQUAL branches halve, R/2R/2, 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.

R1R2Rt

Rt=R1+R2R_{t} = R_{1} + R_{2}

  • RtR_{t}= Total resistance
  • R1R_{1}= Resistance 1
  • R2R_{2}= Resistance 2

each variable a resistance

Two Resistors in Series solver →
R1R2Rt

Rt=R1R2R1+R2R_{t} = \frac{R_{1} R_{2}}{R_{1} + R_{2}}

  • RtR_{t}= Total resistance
  • R1R_{1}= Resistance 1
  • R2R_{2}= Resistance 2

each variable a resistance

Two Resistors in Parallel solver →
IRV

V=IRV = I R

  • VV= Voltage (voltage)
  • II= Current (electric current)
  • RR= Resistance (resistance)
Ohm's Law solver →