What is the total resistance of a parallel circuit containing an 18 ohm and a 9 ohm resistor?

To find the total resistance in a parallel circuit, the formula used is based on the reciprocal of the sum of the reciprocals of the individual resistances. For two resistors in parallel, the total resistance (R_total) can be calculated using the formula:

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

In this case, R1 is 18 ohms and R2 is 9 ohms:

1/R_total = 1/18 + 1/9.

To combine these fractions, it's helpful to convert them to a common denominator. The least common multiple of 18 and 9 is 18:

1/18 + 1/9 = 1/18 + 2/18 = 3/18.

Now, taking the reciprocal to find R_total:

R_total = 18/3 = 6 ohms.

Thus, the total resistance of the parallel circuit with an 18 ohm and a 9 ohm resistor is indeed 6 ohms. This demonstrates how the total resistance in a parallel configuration is less than the resistance of the smallest resistor in the circuit, allowing for greater current flow through the circuit.