If eight loudspeakers in parallel each have an impedance of 16 ohms, what is the total impedance of the circuit?

If eight loudspeakers in parallel each have an impedance of 16 ohms, what is the total impedance of the circuit?

• A. 32 ohms
• B. 4 ohms
• C. 6 ohms
• D. 2 ohms

Answer: (A)

To determine the total impedance of multiple loudspeakers connected in parallel, the formula applied is the reciprocal of the sum of the reciprocals of each individual impedance. In this case, since all loudspeakers have the same impedance of 16 ohms, the calculation can be simplified. For N identical resistances in parallel, the total impedance (Z_total) is given by the formula: 1/Z_total = (1/Z1) + (1/Z2) + ... + (1/ZN) In this scenario: 1/Z_total = (1/16 ohms) + (1/16 ohms) + (1/16 ohms) + (1/16 ohms) + (1/16 ohms) + (1/16 ohms) + (1/16 ohms) + (1/16 ohms) Since there are 8 identical speakers, this can be expressed as: 1/Z_total = 8 * (1/16) This simplifies to: 1/Z_total = 8/16 = 1/2 Now, taking the reciprocal to find Z_total: Z_total = 2 ohms Thus, the total impedance of the circuit with eight loudspeakers connected in parallel

To determine the total impedance of multiple loudspeakers connected in parallel, the formula applied is the reciprocal of the sum of the reciprocals of each individual impedance. In this case, since all loudspeakers have the same impedance of 16 ohms, the calculation can be simplified.

For N identical resistances in parallel, the total impedance (Z_total) is given by the formula:

1/Z_total = (1/Z1) + (1/Z2) + ... + (1/ZN)

In this scenario:

1/Z_total = (1/16 ohms) + (1/16 ohms) + (1/16 ohms) + (1/16 ohms) + (1/16 ohms) + (1/16 ohms) + (1/16 ohms) + (1/16 ohms)

Since there are 8 identical speakers, this can be expressed as:

1/Z_total = 8 * (1/16)

This simplifies to:

1/Z_total = 8/16 = 1/2

Now, taking the reciprocal to find Z_total:

Z_total = 2 ohms

Thus, the total impedance of the circuit with eight loudspeakers connected in parallel