A 14-Ω loudspeaker, a 9.0-Ω loudspeaker, and a 3.2-Ω loudspeaker are connected in parallel across the terminals of an amplifier. Determine the equivalent resistance of the three speakers, assuming that they all behave as resistors.

correct

To determine the equivalent resistance of the three speakers connected in parallel, you can use the formula for the total resistance in a parallel circuit. The formula is as follows:

1/X = (1/R1) + (1/R2) + (1/R3) + ...

In this case, X represents the equivalent resistance of the three speakers, R1 represents the resistance of the 14-Ω loudspeaker, R2 represents the resistance of the 9.0-Ω loudspeaker, and R3 represents the resistance of the 3.2-Ω loudspeaker.

Now let's substitute the given values into the formula:

1/X = (1/14) + (1/9) + (1/3.2)

To solve this equation, add the fractions on the right side:

1/X = (9/126) + (14/126) + (39/126)

Combining the fractions gives:

1/X = (9 + 14 + 39) / 126

Simplifying the numerator:

1/X = 62 / 126

To find the value of X, take the reciprocal of both sides:

X = 126 / 62

Evaluating the division results in:

X ≈ 2.03 Ω

Therefore, the equivalent resistance of the three speakers connected in parallel is approximately 2.03 Ω.