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Lesson 30 · Parallel Circuits
More paths, easier trip
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More paths, easier trip

Now give the current a choice: two resistors side by side, each on its own branch, make a parallel circuit. More paths make the trip EASIER, so the total resistance drops below the smallest branch — always. That is your built-in answer check: a parallel total bigger than either branch is wrong before you even look at the working.

For two branches the recipe 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) — same name tags as last lesson: R1R_1 and R2R_2 are the two branches in ohms, RtR_t the one resistance that replaces them both. Try it in your head: 4 Ω beside 12 Ω gives 4816=3 Ω\dfrac{48}{16} = 3\ \Omega — smaller than 4, just as promised.

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 →