Question

Three 30.0Ω resistors are connected in parallel and placed across a 60.0 V potential difference. What is the equivalent resistance of the parallel circuit?
Group of answer choices

10 Ω

30 Ω

60 Ω

0.1 Ω

Answer 1

To find the equivalent resistance \( R_{eq} \) of three 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 three 30.0 Ω resistors:

\[
R_1 = 30.0 \, \Omega
\]
\[
R_2 = 30.0 \, \Omega
\]
\[
R_3 = 30.0 \, \Omega
\]

Substituting the values into the formula gives us:

\[
\frac{1}{R_{eq}} = \frac{1}{30.0} + \frac{1}{30.0} + \frac{1}{30.0}
\]

This simplifies to:

\[
\frac{1}{R_{eq}} = \frac{1}{30.0} + \frac{1}{30.0} + \frac{1}{30.0} = \frac{3}{30.0} = \frac{1}{10.0}
\]

Now, taking the reciprocal:

\[
R_{eq} = 10.0 \, \Omega
\]

Thus, the equivalent resistance of the parallel circuit is:

\[
\boxed{10 \, \Omega}
\]