Final answer:
The formula to determine the total resistance of a parallel circuit with resistances of r1, r2, and r3 is 1/R = 1/r1 + 1/r2 + 1/r3. This takes into account that in a parallel circuit, each resistor experiences the full source voltage, but the current through each varies.
Step-by-step explanation:
The formula you can use to determine the total resistance of a circuit with three components in parallel, having individual resistances of r1, r2, and r3, is represented by option D: 1/R = 1/r1 + 1/r2 + 1/r3. This is because in a parallel circuit, the total resistance is less than the smallest individual resistance and the voltage across each component is the same, but the current through each can vary depending on the resistance.
Using this formula, you can calculate the reciprocal of the total resistance by adding the reciprocals of the individual resistances. Then, by taking the reciprocal of this sum, you will get the total resistance for the parallel circuit.
In a parallel circuit, each resistor has the same full voltage of the source applied to it, but the current flowing through each resistor is different, depending on the resistance. If there are combinations of series and parallel connections, these can be reduced step by step to a single equivalent resistance.