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Consider a resistor of uniform composition and diameter, with length L.
Cut it into two pieces of length L1+L2=L, which will have resistances of
R1 = (rho/A)L1 and R2 = (rho/A)L2.
So R1+R2 = (rho/A)(L1+L2) = (rho/A)L = R
Consider a resistor of uniform composition and diameter, with length L.
Slice it lengthwise into two pieces of area A1+A2=A, which will have
resistances of R1 = (rhoL)/A1 and R2 = (rhoL)/A2.
So 1/R1 +1/R2 = A1 /(rhoL) + A2 / (rhoL) = (A1+A2) / (rhoL) = 1/R
... Does this seem like a reasonable way to introduce series & parallel
resistance? Or perhaps just use it as a way to reinforce the traditional
derivation?
Tim Folkerts