What is the total resistance when three resistors of 6, 12, and 9 ohms are connected in parallel?

To determine the total resistance when resistors are connected in parallel, the formula used is:

1 / R_total = 1 / R1 + 1 / R2 + 1 / R3.

In this case, the resistors have values of 6 ohms, 12 ohms, and 9 ohms.

Using the formula:

1 / R_total = 1 / 6 + 1 / 12 + 1 / 9.

Calculating each term:

• 1/6 = 0.1667

• 1/12 = 0.0833

• 1/9 = 0.1111

Adding these together gives:

1 / R_total = 0.1667 + 0.0833 + 0.1111 = 0.3611.

Now, to find the total resistance (R_total), take the reciprocal of 0.3611:

R_total = 1 / 0.3611 ≈ 2.77 ohms.

This confirms that the total resistance when three resistors of 6, 12, and 9 ohms are connected in parallel is approximately 2.77 ohms, which aligns with the