What is the value of the third resistor if two parallel resistors of 3 ohms and 6 ohms have a total current flow of 12 amperes?

To find the value of the third resistor when two parallel resistors of 3 ohms and 6 ohms are involved in a circuit with a total current flow of 12 amperes, we first need to understand how resistors behave in parallel.

In a parallel circuit, the total resistance can be calculated using the formula for parallel resistors. The formula for total resistance (R_total) in parallel is given by:

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

For this case, the two resistors are 3 ohms and 6 ohms. We first calculate the resistance of these two:

1/R_total = 1/3 + 1/6.

Finding a common denominator (which is 6):

1/R_total = (2 + 1) / 6 = 3/6 = 1/2.

Thus, R_total for the 3 ohm and 6 ohm resistors is:

R_total = 2 ohms.

Now we know that the total resistance for the two resistors alone is 2 ohms, but the question mentions the total current flow is 12 amperes. We can use Ohm’s Law (V =