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.
Answer: (1/14)+(1/9)+(1/3.2) = (1/X)
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.