Answered: The headphones have a resistanceof 600Ω…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Question

The headphones have a resistance
of 600Ω . The headphone amplifier in a battery-powered device
is designed to deliver 0.1 W to the headphones. If the
resistance of the headphones is 24 , calculate the
voltage and current required from the dependent
voltage source (A_v in our model) to deliver 0.1 W
to the headphones. How much power is delivered
from dependent source? How much power is lost in
the output resistance?

Expert Solution

Step 1

Consider the expression for current,

$I_{0} = \sqrt{\frac{2 P_{0}}{R_{L}}}$

Where,

$P_{0}$ is headphone output power

$R_{L}$ is load resistor

Now putting the value in above equation,

$I_{0} = \sqrt{\frac{2 (0.1)}{600}} = \sqrt{0.33 \times 10^{- 3}} = 18.25 m A$

Step 2

Now expression for the voltage,

$V = I_{0} R = I_{0} (R_{L} + R_{I}) = 18.25 \times 10^{- 3} (600 + 28) = 11.46 V$

Expression for the delivered power,

$P_{D} = \frac{I_{0} V}{2} = \frac{18.25 \times 10^{- 3} (11.46)}{2} = 104.6 \times 10^{- 3} = 104.6 m W$

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