What is the total resistance of this parallel circuit: R1 = 12, R2 = 12, R3 = 12?

To determine the total resistance of a parallel circuit with resistors R1, R2, and R3 all equal to 12 ohms, one can use the formula for calculating total resistance in a parallel configuration. The formula is given by the reciprocal of the total resistance (R_total):

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

In this specific case, all resistors have the same value:

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

1/R_total = 3/12

1/R_total = 1/4

To find R_total, take the reciprocal of 1/4:

R_total = 4 ohms

Thus, the total resistance of the circuit is 4 ohms. This makes sense considering that in a parallel configuration, the total resistance is always less than the smallest resistance in the circuit. So, even though each resistor is 12 ohms, the effective resistance decreases due to the parallel arrangement.

This helps to confirm that 4 ohms is indeed the correct answer for the total resistance in this scenario.