Final answer:
The resistance of the third resistor in a series circuit with a total resistance of 9 ohms, where the other two resistors have resistances of 3 ohms and 2 ohms, is 4 ohms.
Step-by-step explanation:
When resistors are connected in series, the total resistance of the circuit is the sum of the individual resistances. In the given problem, we have three resistors in series with a total resistance of 9 ohms, and we already know the resistance of two of these resistors: 3 ohms and 2 ohms.
To find the resistance of the third resistor (let's call it R3), we use the formula for resistors in series:
total resistance = R1 + R2 + R3
Substituting the known values, we get:
9 ohms = 3 ohms + 2 ohms + R3
Which simplifies to:
9 ohms = 5 ohms + R3
Therefore, the resistance of the third resistor is:
R3 = 9 ohms - 5 ohms = 4 ohms.
So, the third resistor has a resistance of 4 ohms.