(a) Explanation Given Info: For an L-R-C series circuit, the resistance of the resistor 200 Ω . The inductance of the inductor is 0.9 H . The capacitance of the capacitor is 6 μF . The voltage amplitude is 30 V , and an angular frequency is 250 rad / s . Consider the formula for the inductive reactance X L . X L = ω L ω is the angular frequency, L is the inductance of the inductor, Substitute 250 rad / s for ω and 0.9 H for L to find X L . X L = ( 250 rad / s ) ( 0.9 H ) = 225 Ω Consider the formula for the capacitive reactance X C . X C = 1 ω C ω is the angular frequency, C is the capacitance of the capacitor. Substitute 250 rad / s for ω and 6 × 10 − 6 F for C to find X C . X C = 1 ( 250 rad / s ) ( 6 × 10 − 6 F ) = 666.7 Ω Consider the formula for magnitude of impedance in L-R-C series circuit. Z = R 2 + ( X L − X C ) 2 R is the resistance of the circuit, X L is the inductive reactance of the circuit, X C is the capacitive reactance of the circuit. Substitute 200 Ω for R , 225 Ω for X L , and 666.7 Ω for to find Z . Z = ( 200 Ω ) 2 + ( ( 225 Ω ) − ( 666.7 Ω ) ) 2 = ( 200 Ω ) 2 + ( − 441.7 Ω ) 2 = 484.9 Ω Consider the formula for source voltage in an L-R-C series circuit. V = I Z I is the current flowing through the circuit, Z is the impedance of the circuit. Rearrange the equation to find I . I = V Z Substitute 30 V for V and 484.9 Ω for Z to find I . I = 30 V 484.9 Ω = 0.06187 A = 61.87 × 10 − 3 A = 61.87 mA Consider the formula for the instantaneous voltage across the resistor. v R = V R cos ( ω t ) (I) V R is the voltage across the resistor, ω is the angular frequency, t is the time period. Consider the formula for voltage across the resistor. V R = I R (II) I is the current through the resistor, R is the resistance of the resistor. Substitute I R for V R in equation (I). v R = I R cos ( ω t ) Substitute 61.87 × 10 − 3 A for I , 200 Ω for R , 250 rad / s for ω and 20 × 10 − 3 s for t to find v R . v R = ( 61.87 × 10 − 3 A ) ( 200 Ω ) cos [ ( 250 rad / s ) ( 20 × 10 − 3 s ) ] = 3 (b) To determine The values of V R , V L , V C and to check whether V R + V L + V C is equal to v .

University Physics with Modern Physics (14th Edition)

14th Edition

ISBN: 9780321973610

Author: Hugh D. Young, Roger A. Freedman

Publisher: PEARSON

See similar textbooks

Concept explainers

Electromagnets

The word "electromagnet" is composed of two words, ‘electro’ and ‘magnet’. It is a type of magnet in which an electric current helps in the generation of a magnetic field. Electromagnets usually consist of two major parts, wire and a coil around which th…

Question

Chapter 31, Problem 31.16E

(a)

To determine

The values of v, vR , vL and vC at t=20 ms .

(b)

To determine

The values of VR , VL , VC and to check whether VR+VL+VC is equal to v .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 31, Problem 31.15E

Chapter 31, Problem 31.17E

Students have asked these similar questions

Hi, 1- Does Quantum physics theory and Newtowin physics right or wrong about Gravity? 2- How can we rewrite Quantum physics and Newtowin physics Equations?

Hi Expert in Physics, Could you please Rewrite thses random equations using good formula of mathematics and explain each Greek alphabet and their meaning in English? Best Regards, Yahya

Hi Expert, I have uploaded picture, could you please name the Greek alphabet and their name in English?

Chapter 31 Solutions

University Physics with Modern Physics (14th Edition)

Ch. 31.1 - The accompanying figure shows four different...Ch. 31.2 - An oscillating voltage of fixed amplitude is...Ch. 31.3 - Rank the following ac circuits in order of their...Ch. 31.4 - Prob. 31.4TYU Ch. 31.5 - How does the resonance frequency of an L-R-C...Ch. 31.6 - Each of the following four transformers has 1000...Ch. 31 - Household electric power in most of western Europe...Ch. 31 - The current in an ac power line changes direction...Ch. 31 - In an ac circuit, why is the average power for an...Ch. 31 - Equation (31.14) was derived by using the...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

The values of v , v R , v L and v C at t = 20 ms .

Solution Summary: The author explains the formula for the inductive reactance X_L for an L-R-C series circuit.

Concept explainers

The values of v, vR , vL and vC at t=20 ms .

The values of VR , VL , VC and to check whether VR+VL+VC is equal to v .

Want to see the full answer?

Chapter 31 Solutions