What is the equivalent resistance in a parallel circuit that has the following three resistors: 6.8 ohms, 9.0 ohms, and 15.0 ohms?

Question

A.
10.3 ohms
B.
30.8 ohms
C.
3.08 ohms
D.
0.80 ohms
E.
12.8 ohms

Answer 1

To find the equivalent resistance \( R_{eq} \) for resistors in parallel, you use the formula:

\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \]

where \( R_1 = 6.8 , \Omega \), \( R_2 = 9.0 , \Omega \), and \( R_3 = 15.0 , \Omega \).

Calculating each term:

\[ \frac{1}{R_1} = \frac{1}{6.8} \approx 0.1471 \] \[ \frac{1}{R_2} = \frac{1}{9.0} \approx 0.1111 \] \[ \frac{1}{R_3} = \frac{1}{15.0} \approx 0.0667 \]

Now, summing these values:

\[ \frac{1}{R_{eq}} = 0.1471 + 0.1111 + 0.0667 \approx 0.3250 \]

Now, take the reciprocal to find \( R_{eq} \):

\[ R_{eq} = \frac{1}{0.3250} \approx 3.08 , \Omega \]

Thus, the equivalent resistance of the parallel circuit is approximately \( 3.08 , \Omega \).

The correct answer is \( \text{C. } 3.08 , \Omega \).