If three resistors are connected in parallel with two at 12 ohms and one at 6 ohms, what is the total resistance?

To determine the total resistance of resistors connected in parallel, you can use the formula for parallel resistance, which is given by:

[

\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}

]

In this scenario, you have two resistors at 12 ohms (let's call them R1 and R2) and one resistor at 6 ohms (R3).

Substituting the values into the formula, you get:

[

\frac{1}{R_{total}} = \frac{1}{12} + \frac{1}{12} + \frac{1}{6}

]

To add these fractions together, it's helpful to find a common denominator. The least common multiple of 12 and 6 is 12:

[

\frac{1}{R_{total}} = \frac{1}{12} + \frac{1}{12} + \frac{2}{12}

]

This simplifies to:

[

\frac{1}{R_{total}} = \frac{1 + 1 + 2}{12} =