resistors in parallel
Resistors in parallel are connected side by side, both of their ends tied together, so they share the same two nodes. Picture extra lanes added to a highway: each lane gives the traffic another way through, so together they carry more total flow than any single lane could. Because both ends are common, every parallel resistor feels the exact same voltage across it, and the incoming current splits among them.
Adding paths can only make it easier for current, so the combined resistance is always smaller than the smallest branch. The rule is 1/R_total = 1/R1 + 1/R2 + ..., and for just two resistors there is a neat shortcut: R_total = R1 times R2 / (R1 + R2), often called the product over sum. Two equal resistors in parallel give exactly half: 100 ohm with 100 ohm is 50 ohm. A 1 kohm with a 1 kohm is 500 ohm, and a 1 kohm with a 10 kohm is about 909 ohm, just a touch below the smaller one.
You reach for parallel resistors to make odd in-between values, to share current and therefore heat across several parts, or to lower a resistance you find is too high. The mirror image of series applies: parallel resistors share the same voltage but split the current. The surprise for beginners is that the parallel total drops below even the smallest resistor in the group, which feels backwards until the highway picture clicks.
Two 1 kohm resistors in parallel give 1000 times 1000 / (1000 + 1000) = 500 ohm, and they share the load: each carries half the current, so each dissipates half the heat one resistor alone would have.
Product over sum gives two-resistor parallel values fast; equal pairs simply halve.
A parallel combination is always smaller than its smallest member. If your answer is bigger than any branch, you used the series rule by mistake.