Chapter 35, Problem 51A

A $16\text{-}\Omega$ loudspeaker and an $8\text{-}\Omega$ loudspeaker are connected in parallel across the terminals of an amplifier. Assuming the speakers behave as resistors, calculate the equivalent resistance of the two speakers.

To determine

The equivalent resistance of two speakers in parallel.

Answer to Problem 51A

The equivalent resistance two speakers is $5.33\Omega$ .

Explanation of Solution

Given info:

Resistance of first speaker, $R_1=16\Omega$

Resistance of second speaker, $R_2=8\Omega$

Formula used:

The expression to calculate the equivalent resistance of two speakers is,

  $R_p=\frac{R_1{R}_2}{R_1+R_2}$

Calculation:

Substitute the given values in the above expression.

  $\begin{array}{c}{R}_p=\frac{\left(16\Omega \right)\left(8\Omega \right)}{16\Omega +8\Omega }\\ =5.33\Omega \end{array}$

Conclusion:

The equivalent resistance two speakers is $5.33\Omega$ .