Problem-Solving Strategy 19.1 Resistors in series and in parallel SET UP It helps to remember that when resistors are connected in series, the total potential difference across the combination is the sum of the individual potential differences. When resistors are connected in parallel, the potential difference is the same for every resistor and is equal to the potential difference across the parallel combination. Also, keep in mind the analogous statements for current: When resistors are connected in series, the current is the same through every resistor and is equal to the current through the series combination. When resistors are connected in parallel, the total current through the combination is equal to the sum of currents through the individual resistors. SOLVE We can often consider complicated networks to be combinations of series and parallel arrangements. We then replace each simple series or parallel combination by its equivalent resistance. REFLECT The rule for combining resistors in parallel follows directly from the principle of conservation of charge. The rule for combining resistors in series results from a fundamental principle about work: When a particle moves along a path, the total work done on it is the sum of the quantities of work done during the individual segments of the path. SET UP