We spent most of today talking about conductance whereas resistance is what is used most of the time. Since currents are the desired product I believe it makes more sense to think in terms of what makes a current flow rather than what prevents it. Resistance is merely the inverse of conductance. Instead of I = delta V x Conductance it is usually written as I = delta V/Resistance or more commonly V/R.
Since conductances add when in parallel; inverses of resistance add in parallel
Rpar =1/(1/R1+1/R2). Since inverses of conductances add when in series; resistances add in series
R series = R1+R2.
Circuit problems are solved by finding equivalent resistances or conductances for the combined elements in the circuit. It is easiest to think of adding parallel conductances to get the equivalent conductances for those elements in parallel. Then take the inverse of those conductances and add to the other elements in series with them.
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