Why do most textbooks use the inverse formula 1/rtotal for parallel resistance?
Why is this form so commonly presented?


Sometimes, when faced with several parallel resistors it's easier to think in terms of conductance (amps per volt) rather than resistance (volts per amp). So, we convert each resistance (R) to conductance (G) and add them. Then we convert back to resistance by inverting the summed conductance value.

Forgetting that you were working with conductances is just a memory fault.

\$\dfrac{1}{R_T}\$ is just \$G_T\$ and,

\$G_T = G_1+G_2+G_3+G_4\$

Where \$G_n = \dfrac{1}{R_n}\$

With parallel resistors they all share the same voltage and therefore, asking the question how many amps do we get for a given voltage (conductance) is much more relevant than asking how many volts per amp. In fact, asking how many volts per amp is confusing when you have parallel components because, they all share the same voltage.

Of course, with series resistors, it’s totally relevant to ask how many volts per amp because, current is common to all series components.