Resistance of Conductors in Series and Parallel

n The total resistance of any number of resistances joined in series is the sum of the separate resistances. The total resistance of conductors in parallel whose separate resistances are r ₁, r ₂, r ₃…r _n is given by the formula

$${1 \over R} = {1 \over {r_1 }} + {1 \over {r_2 }} + {1 \over {r_3 }} \cdot _{} \cdot _{} \cdot _{} \cdot _{} + {1 \over {r_{\rm n} }}$$

Where R is the total resistance. For two terms this becomes,

$$R = {r_{1} r_2 \over r_1 + r_2 }$$

(Lide DR (ed) (2004) CRC handbook of chemistry and physics. CRC Press, Boca Raton, FL; Giambattista A, Richardson R, Richardson RC, Richardson B (2003) College physics. McGraw-Hill Science/Engineering/Math, New York).