/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 25 31.25. The power of a certain CD... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 31: Problem 25

31.25. The power of a certain CD player operating at 120 \(\mathrm{V}\) rms is 20.0 \(\mathrm{W}\) . Assuming that the CD player behaves like a pure resistance, find (a) the maximum instantancous power; (b) the rms current; (c) the resistance of this player.

Short Answer

Expert verified
(a) 40.0 W (b) 0.167 A (c) 719.16 惟

Step by step solution

01

Understand the Given Information

We are given a CD player with an RMS voltage of 120 V and power of 20.0 W. We need to find the maximum instantaneous power, the RMS current, and the resistance of the CD player.
02

Calculate the RMS Current

Use the formula for power in terms of RMS values: \( P = V_{rms} \times I_{rms} \). Given that \( P = 20.0 \, \text{W} \) and \( V_{rms} = 120 \, \text{V} \), we can solve for the RMS current \( I_{rms} \):\[ I_{rms} = \frac{P}{V_{rms}} = \frac{20.0}{120} = 0.167 \, \text{A} \]
03

Determine the Maximum Instantaneous Power

The maximum instantaneous power \( P_{max} \) in a resistive circuit can be found using the formula \( P_{max} = V_{max} \times I_{max} \). Since \( V_{max} = \sqrt{2} \times V_{rms} \) and \( I_{max} = \sqrt{2} \times I_{rms} \), the formula becomes:\[ P_{max} = 2 \times V_{rms} \times I_{rms} = 2 \times 20.0 = 40.0 \, \text{W} \]
04

Calculate the Resistance

To find the resistance of the CD player, use Ohm's law with RMS values: \( V_{rms} = I_{rms} \times R \).Rearranging gives us \( R = \frac{V_{rms}}{I_{rms}} = \frac{120}{0.167} \approx 719.16 \, \text{惟} \).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

RMS voltage
RMS voltage, or root mean square voltage, is a crucial concept in AC circuit analysis. It represents the effective value of a varying voltage waveform, which in this case is AC.
RMS voltage is particularly useful because it allows us to calculate power in AC circuits in a manner similar to how we do so in DC circuits. For sinusoidal waveforms, the RMS voltage is calculated as follows:
    \( V_{rms} = \frac{V_{max}}{\sqrt{2}}, \)
where \( V_{max} \) is the maximum (peak) voltage.
By standardizing AC voltage to its RMS value, we can directly compare it to DC voltage and use familiar equations, like Ohm鈥檚 Law.
RMS current
RMS current is similar to RMS voltage and represents the effective current flowing through an AC circuit. Just as with RMS voltage, RMS current is a crucial value for calculating power in AC circuits.
It is defined as:
    \( I_{rms} = \frac{I_{max}}{\sqrt{2}}, \)
where \( I_{max} \) is the peak current.
In AC circuits, the RMS current allows us to apply Ohm鈥檚 Law in a straightforward way:
    \( I_{rms} = \frac{P}{V_{rms}}, \)
making it easy to determine current when we know power \( P \) and RMS voltage \( V_{rms}. \)
Ohm's Law
Ohm鈥檚 Law forms the backbone of circuit analysis by linking voltage, current, and resistance. In simple terms, it states that the voltage (V) across a conductor in a circuit is directly proportional to the current (I) flowing through it, provided the temperature remains constant.
The formula is:
    \( V = I \times R, \)
where \( R \) is the resistance.
This law applies to resistive circuits and can be utilized with RMS values in AC circuits. By rearranging the formula to \( R = \frac{V_{rms}}{I_{rms}}, \) we can determine the resistance in a circuit. Ohm's Law is fundamental in understanding how circuits operate and troubleshooting them.
resistive circuit
A resistive circuit is one that primarily contains resistors, and as its name implies, it resists the flow of electrical current. The components in such circuits follow Ohm鈥檚 Law exclusively.
In AC analysis, resistive circuits simplify calculations because the current and voltage waveforms remain perfectly in phase. This means the peaks of the voltage and current waves line up with each other.
In our exercise, the assumption is that the CD player acts like a pure resistive load. This justifies using simple RMS calculations to understand current flow and power consumption.
power calculation
Power calculation in AC circuits, particularly for resistive loads, is an important aspect of circuit analysis. In a resistive circuit, power can be calculated using several formulas depending on known values. The most common formula uses RMS values:
    \( P = V_{rms} \times I_{rms}. \)

This gives the average power consumed over time. If you want the maximum instantaneous power (power peaks), you'd calculate:
    \( P_{max} = 2 \times V_{rms} \times I_{rms}. \)

Understanding these formulas allows for precise management of energy use and efficiency in electronic devices.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

31.47. An \(L-R-C\) series circuit consists of a \(50.0-\Omega\) resistor, a \(10.0-\mu\) F capacitor, a \(3.50-\mathrm{mH}\) inductor, and an ac voltage source of voltage anplitude 60.0 \(\mathrm{V}\) operating at 1250 \(\mathrm{Hz}\) (a) Find the current amplitude and the voltage amplitudes across the inductor, the resistor, and the capacitor. Why can the voltage amplitudes add up to more than 60.0 \(\mathrm{V} ?\) (b) If the frequency is now doubled, but nothing else is changed, which of the quantities in part (a) will change? Find the new values for those that do change.

31.28. An L-R-C series circuit is connected to a \(120-\mathrm{Hz}\) ac source that has \(V_{\mathrm{rms}}=80.0 \mathrm{V}\) . The circuit has a resistance of 75.0\(\Omega\) and an impedance at this frequency nf 105\(\Omega\) . What average power is delivered to the circuit by the source?

31.33. In an \(L . R-C\) series circuit, \(R=150 \Omega, L=0.750 \mathrm{H},\) and \(C=0.0180 \mu \mathrm{F} .\) The source has voltage amplitude \(V=150 \mathrm{V}\) and a frequency equal to the resonance frequency of the circuit. (a) What is the power factor? (b) What is the average power delivered by the source? (c) The capacitor is replaced by one with \(C=0.0360 \mu \mathrm{F}\) and the source frequency is adjusted to the new resonance value. Then what is the average power delivered by the source?

31.65. An inductor, a capacitor, and a resistor are all connected in series across an ac source. If the resistance, inductance, and capacitance are all doubled, by what factor does each of the following quantities change? Indicate whether they increase or decrease: (a) the resonance angular frequency; (b) the inductive reactance; (c) the capacitive reactance. (d) Does the impedance double?

31.23. In an \(L-R-C\) series circuit, the rms voltage across the resistor is 30.0 \(\mathrm{V}\) , across the capacitor it is 90.0 \(\mathrm{V}\) , and across the inductor it is 50.0 \(\mathrm{V}\) . What is the rms voltage of the source?
See all solutions

Recommended explanations on Physics Textbooks

Physical Quantities And Units

Read Explanation

Force

Read Explanation

Physics of Motion

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation

Electricity and Magnetism

Read Explanation

Waves Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.