What is the formula for the total resistance when R1, R2, and R3 are connected in parallel?

The total resistance for resistors connected in parallel is given by the formula that includes the reciprocals of each individual resistor's resistance. When R1, R2, and R3 are connected in parallel, the total resistance ( R_t ) is computed using the formula:

[

\frac{1}{R_t} = \frac{1}{R1} + \frac{1}{R2} + \frac{1}{R3}

]

This can be rearranged to express ( R_t ):

[

R_t = \frac{1}{\left(\frac{1}{R1} + \frac{1}{R2} + \frac{1}{R3}\right)}

]

This formula ensures that the total resistance decreases as more resistors are added in parallel, which is a characteristic behavior of parallel circuits. Each additional path for current flow provides more options for current, thereby reducing the overall resistance.

The other formulas presented don’t represent the correct method for combining resistances in parallel. For example, the formula that sums the resistances directly, like ( R1 + R2 + R3 ), applies to series circuits, where the total resistance increases as resistors are added. The