To find the equivalent resistance (R_eq) in a parallel circuit, you can use the formula:
\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \]
where \(R_1\), \(R_2\), and \(R_3\) are the resistances of the individual resistors.
In this case, we have:
- \(R_1 = 6.8 , \text{ohms}\)
- \(R_2 = 9.0 , \text{ohms}\)
- \(R_3 = 15.0 , \text{ohms}\)
Calculating the reciprocal of each resistance:
\[ \frac{1}{R_1} = \frac{1}{6.8} \approx 0.14706 \] \[ \frac{1}{R_2} = \frac{1}{9.0} \approx 0.11111 \] \[ \frac{1}{R_3} = \frac{1}{15.0} \approx 0.06667 \]
Now, add these values together:
\[ \frac{1}{R_{eq}} = 0.14706 + 0.11111 + 0.06667 \approx 0.32484 \]
Now, we take the reciprocal of this sum to find \(R_{eq}\):
\[ R_{eq} \approx \frac{1}{0.32484} \approx 3.08 , \text{ohms} \]
So the equivalent resistance is approximately 3.08 ohms.
Thus, the correct answer is:
C. 3.08 ohms