(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, Volume 2 (Chs. 21-37); Mastering Physics with Pearson eText -- ValuePack Access Card (14th Edition)

14th Edition

ISBN: 9780134265414

Author: Hugh D. Young, Roger A. Freedman

Publisher: PEARSON

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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 .

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Chapter 31, Problem 31.15E

Chapter 31, Problem 31.17E

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University Physics with Modern Physics, Volume 2 (Chs. 21-37); Mastering Physics with Pearson eText -- ValuePack Access Card (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...

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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.

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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 .

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Chapter 31 Solutions