Explanation Formula used: For L − R − C circuit, the initial value problem for charge is given by, L d 2 Q d t 2 + R d Q d t + 1 C Q = E ( t ) , with initial conditions, Q ( 0 ) = 0 I ( 0 ) = d Q d t ( 0 ) = 0 where, L , C and R are inductance, capacitance and resistance of the circuit respectively and E ( t ) is the voltage impressed on the circuit. The reactance of the L − R − C circuit is given by the formula, L ω − 1 / ( C ω ) . and impedance of the circuit is, ( L ω − 1 / ( C ω ) ) 2 + R 2 and both are measured in o h m s . Calculation: For the given problem, the initial value problem for charge is, 1 d 2 Q d t 2 + 40 d Q d t + 1 1 4000 Q = 24 sin 4 t d 2 Q d t 2 + 40 d Q d t + 4000 Q = 24 sin 4 t The corresponding characteristics equation of the homogeneous equation is, r 2 + 40 r + 4000 = 0 The solution of the above characteristics equation is given by, r 1 , 2 = − 40 ±

5th Edition

ISBN: 9780128149485

Author: Abell, Martha L. L.

Publisher: Elsevier Science

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Chapter 5.4, Problem 18E

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The reactance and the impedance of the circuit

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Chapter 5.4, Problem 17E

Chapter 5.4, Problem 19E

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Chapter 5 Solutions

Introductory Differential Equations

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