Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 21: Problem 64

For a particular \(R L C\) series circuit, the capacitive reactance is $12.0 \Omega,\( the inductive reactance is \)23.0 \Omega,$ and the maximum voltage across the \(25.0-\Omega\) resistor is \(8.00 \mathrm{V}\) (a) What is the impedance of the circuit? (b) What is the maximum voltage across this circuit?

Short Answer

Expert verified
Answer: The impedance of the circuit is approximately 27.3Ω, and the maximum voltage across the circuit is approximately 8.74V.

Step by step solution

01

Find the Impedance

First, we need to find the impedance of the circuit. Use the formula: \(Z = \sqrt{R^2 + (X_L - X_C)^2}\), where \(R = 25.0\Omega\), \(X_L = 23.0\Omega\), and \(X_C = 12.0\Omega\). Calculating the impedance: \(Z = \sqrt{(25.0)^2 + (23.0 - 12.0)^2} = \sqrt{625 + 121} = \sqrt{746} \approx 27.3\Omega\) So, the impedance of the circuit is approximately \(27.3\Omega\).
02

Find the Maximum Current

Now, we need to find the maximum current in the circuit. Use the formula: \(I_{max} = \frac{V_R}{R}\), where \(V_R = 8.00V\) and \(R = 25.0\Omega\). Calculating the maximum current: \(I_{max} = \frac{8.00}{25.0} = 0.32A\) Therefore, the maximum current in the circuit is \(0.32A\).
03

Find the Maximum Voltage across the Circuit

Lastly, we need to find the maximum voltage across the circuit. Use the formula: \(V_{max} = I_{max} \cdot Z\), where \(I_{max} = 0.32A\) and \(Z \approx 27.3\Omega\). Calculating the maximum voltage: \(V_{max} = 0.32 \cdot 27.3 \approx 8.74V\) Hence, the maximum voltage across the circuit is approximately \(8.74V\).

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

An RLC series circuit is driven by a sinusoidal emf at the circuit's resonant frequency. (a) What is the phase difference between the voltages across the capacitor and inductor? [Hint: since they are in series, the same current \(i(t) \text { flows through them. }]\) (b) At resonance, the rms current in the circuit is \(120 \mathrm{mA}\). The resistance in the circuit is \(20 \Omega .\) What is the rms value of the applied emf? (c) If the frequency of the emf is changed without changing its rms value, what happens to the rms current? (W) tutorial: resonance)
Suppose that an ideal capacitor and an ideal inductor are connected in series in an ac circuit. (a) What is the phase difference between \(v_{\mathrm{C}}(t)\) and \(v_{\mathrm{L}}(t) ?\) [Hint: since they are in series, the same current \(i(t)\) flows through both. \(]\) (b) If the rms voltages across the capacitor and inductor are \(5.0 \mathrm{V}\) and \(1.0 \mathrm{V}\), respectively, what would an ac voltmeter (which reads rms voltages) connected across the series combination read?
What is the rins current flowing in a \(4.50-\mathrm{kW}\) motor connected to a \(220-\mathrm{V}\) rms line when (a) the power factor is 1.00 and (b) when it is \(0.80 ?\)
A lightbulb is connected to a \(120-\mathrm{V}\) (rms), \(60-\mathrm{Hz}\) source. How many times per second does the current reverse direction?
A solenoid with a radius of \(8.0 \times 10^{-3} \mathrm{m}\) and 200 turns/cm is used as an inductor in a circuit. When the solenoid is connected to a source of \(15 \mathrm{V}\) ms at \(22 \mathrm{kHz}\), an \(\mathrm{rms}\) current of \(3.5 \times 10^{-2} \mathrm{A}\) is measured. Assume the resistance of the solenoid is negligible. (a) What is the inductive reactance? (b) What is the length of the solenoid?
See all solutions

Recommended explanations on Physics Textbooks

Wave Optics

Read Explanation

Electrostatics

Read Explanation

Medical Physics

Read Explanation

Modern Physics

Read Explanation

Circular Motion and Gravitation

Read Explanation

Electric Charge Field and Potential

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.

Sign-up for free