Resistors of 10, 15, and 6 ohms are connected in parallel. What is the total resistance?

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

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

In this case, the resistors have values of 10 ohms, 15 ohms, and 6 ohms. Applying the formula, we first calculate the reciprocal of each resistance:

1. For the 10 ohm resistor: 1 / 10 = 0.1

2. For the 15 ohm resistor: 1 / 15 ≈ 0.0667

3. For the 6 ohm resistor: 1 / 6 ≈ 0.1667

Next, we sum these values:

0.1 + 0.0667 + 0.1667 ≈ 0.3334

Now, to find the total resistance, you take the reciprocal of this sum:

R_total = 1 / 0.3334 ≈ 3 ohms

Thus, the total resistance of the resistors connected in parallel is approximately 3 ohms. This aligns with the correct answer choice. The calculations show how the total resistance decreases when resistors are joined