Final answer:
The equivalent resistance for the circuit with two 6 ohm resistors in series and one 12 ohm resistor in parallel is 10 ohms.
Step-by-step explanation:
The equivalent resistance of a circuit with resistors in both series and parallel can be calculated by first finding the resistance of the parallel section and then adding it to the resistance of the series section. Assuming two 6 ohm resistors are connected in series and a 12 ohm resistor is connected in parallel with one of the 6 ohm resistors, we calculate the total resistance as follows:
First, we find the resistance of the 6 ohm resistor in parallel with the 12 ohm resistor using the formula for parallel resistance:
1/Rp = 1/R2 + 1/R3, where Rp is the equivalent parallel resistance, R2 = 6 ohms, and R3 = 12 ohms. So, 1/Rp = 1/6 + 1/12 = 2/12 + 1/12 = 3/12. Thus, Rp = 12/3 = 4 ohms.
Next, we add the resistance of the first 6 ohm resistor which is in series with the equivalent parallel resistance (Rp) to get the total resistance (Rtot): Rtot = R1 + Rp, where R1 is the series resistance of 6 ohms, thus Rtot = 6 + 4 = 10 ohms.
The total equivalent resistance of the circuit is therefore 10 ohms.