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?

Question

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:

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