When you wire two resistors in parallel, you can calculate the total resistance using the following formula:
1 / R_total = 1 / R1 + 1 / R2
Where R_total is the total resistance, R1 is the resistance of the first resistor, and R2 is the resistance of the second resistor.
In your case, you have a 6-ohm resistor (R1) and an 8-ohm resistor (R2) wired in parallel, so you can plug these values into the formula:
1 / R_total = 1 / 6 ohms + 1 / 8 ohms
Now, let's calculate it step by step:
1 / R_total = (1 / 6) + (1 / 8 )
To add these fractions, you need a common denominator, which is 24. So, you can rewrite the fractions with the common denominator:
1 / R_total = (4/24) + (3/24)
Now, add the fractions:
1 / R_total = (4/24 + 3/24) = 7/24
Now, take the reciprocal of both sides to find R_total:
R_total = 24 / 7 ohms
So, when you wire a 6-ohm and an 8-ohm resistor in parallel, the total resistance is approximately 3.43 ohms.