Question

Four eight-ohm speakers are connected in parallel to an audio power amplifier. The amplifier can supply a maximum driver output voltage of fifteen volts. How much audio power must the amplifier be able to deliver to the speakers when outputting this maximum voltage?

Answer 1

112.5 watts

Step-by-step explanation:

The output voltage (V) = 15 volts

The equivalent resistance for the speakers connected in parallel (
`R_T`) is gotten by using the formula:

`(1)/(R_T)=(1)/(R_1)+(1)/(R_2)+(1)/(R_3)+(1)/(R_4)\\\\But\ R_1=R_2=R_3=R_4=8\ ohm\\\\(1)/(R_T) =(1)/(8) +(1)/(8) +(1)/(8) +(1)/(8) \\\\(1)/(R_T) =(1+1+1+1)/(8) \\\\(1)/(R_T) =(4)/(8) \\\\R_T=(8)/(4) \\\\R_T=2\ ohm`

The current flowing through the amplifier (I) is:

I = V /
`R_T` = 15 / 2 = 7.5 A

The audio power (P) when outputting this maximum voltage is given by:

P = V² /
`R_T` = I²
`R_T`. Therefore:

P = V² /
`R_T` = 15² /
`R_T` = 112.5 watts