**Problem Statement:**A series RCL circuit contains a 76.3-Ω resistor, a 2.92-μF capacitor, and a 4.25-mH inductor. When the frequency is 2600 Hz, what is the power factor of the circuit?**Input Fields:**- **Number**: [ Input Box ]- **Units**: [ Dropdown Menu ]---**Explanation:**In this problem, we aim to find the power factor of an RCL circuit with given components when operating at a specific frequency. For an RCL circuit, the power factor (PF) is given by the cosine of the phase angle (φ) between the total voltage and the total current. The phase angle φ can be calculated using the impedance values of the resistor (R), capacitor (C), and inductor (L).### Step-by-Step Solution:1. **Calculate Impedance of the Capacitor (Xc):** - Formula: \( X_c = \frac{1}{2\pi f C} \) - \( C = 2.92 \times 10^{-6} \, F \) (convert μF to F)2. **Calculate Impedance of the Inductor (Xl):** - Formula: \( X_l = 2\pi f L \) - \( L = 4.25 \times 10^{-3} \, H \) (convert mH to H)3. **Calculate Net Reactance (X):** - Formula: \( X = X_l - X_c \)4. **Calculate Total Impedance (Z):** - Formula: \( Z = \sqrt{R^2 + X^2} \)5. **Calculate Phase Angle (φ):** - Formula: \( \tan{\phi} = \frac{X}{R} \) - Use the arctangent function to find φ: \( \phi = \tan^{-1}(\frac{X}{R}) \)6. **Calculate Power Factor (PF):** - Formula: \( PF = \cos{\phi} \)Ensure to substitute the calculated values at each step to maintain accuracy.**Note: If the power factor is lagging or leading depends on whether the circuit is more inductive or capacitive, respectively.**

Given : Resistance (R) = 76.3 Ω Capacitance(C) = 2.92 μF = 2.92*10-6 F Inductance(L) = 4.25 mH =…

Answered: A series RCL circuit contains a 76.3-…

A series RCL circuit contains a 76.3- resistor, a 2.92-µF capacitor, and a 4.25-mH inductor. When the frequency is 2600 Hz, what is the power factor of the circuit?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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