The total resistance of a group of resistors in parallel is found by adding up the reciprocals of the resistance values, and then taking the reciprocal of the total.
So for example:
R1=10k Ω, R2=2k Ω, R3=1k Ω
1/10 + 1/2 + 1/1 = 8/5 so the total resistance would be 5/8k Ohms, or 625 Ohms.
Total resistance in a parallel circuit is always less than the smallest resistor in the circuit. This is because you are adding conductors into the circuit when you add a resistor in parallel. And as conductance goes up, resistance goes down. Parallel circuits will continue to operate, though not to full capacity, even if one of the parallel components fail. This happens because the circuit wiring/path also bypasses each component in the circuit.
