A 5.0Ω resistor, a 10.0Ω resistor, and a 15.0Ω resistor are connected in parallel and placed across a potential difference of 30.0 V. What is the equivalent resistance of the parallel circuit?

Question

Group of answer choices

8.3 Ω

0.5 Ω

2.7 Ω

30.6 Ω

Answer 1

To find the equivalent resistance \( R_{eq} \) of resistors connected in parallel, we can use the formula:

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

For the given resistors:

• \( R_1 = 5.0 , \Omega \)
• \( R_2 = 10.0 , \Omega \)
• \( R_3 = 15.0 , \Omega \)

Now, substituting the values into the formula:

\[ \frac{1}{R_{eq}} = \frac{1}{5.0} + \frac{1}{10.0} + \frac{1}{15.0} \]

Calculating each term:

\[ \frac{1}{5.0} = 0.2 \] \[ \frac{1}{10.0} = 0.1 \] \[ \frac{1}{15.0} \approx 0.0667 \]

Now, adding these values together:

\[ \frac{1}{R_{eq}} = 0.2 + 0.1 + 0.0667 \approx 0.3667 \]

Now, we need to find \( R_{eq} \) by taking the reciprocal:

\[ R_{eq} = \frac{1}{0.3667} \approx 2.73 , \Omega \]

Rounding this value to one decimal place gives us \( R_{eq} \approx 2.7 , \Omega \).

Thus, the equivalent resistance of the parallel circuit is:

2.7 Ω