What is the total resistance of three 12-ohm resistors wired in parallel?

What is the total resistance of three 12-ohm resistors wired in parallel?

• A. 6 ohms
• B. 8 ohms
• C. 12 ohms
• D. 4 ohms

Answer: (D)

To determine the total resistance of resistors wired in parallel, the formula used is as follows:

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

For three resistors of equal resistance, this can be simplified. In this case, each resistor has a resistance of 12 ohms. Therefore, the equation would look like this:

1/R_total = 1/12 + 1/12 + 1/12

This simplifies to:

1/R_total = 3/12

To find R_total, you can take the reciprocal of both sides:

R_total = 12/3 = 4 ohms

Thus, the total resistance for the three 12-ohm resistors connected in parallel is 4 ohms. The reasoning emerges from the principle that in a parallel circuit, the total resistance is always less than the smallest resistance present in the circuit, leading to the reduction in total resistance with the addition of more parallel paths.