Explanation Formula used: The governing equation of Kirchhoff’s law is calculated as: L q ″ + R q ′ + 1 C q = E ( t ) . The quadratic equation a x 2 + b x + c = 0 is calculated as x = − b ± b 2 − 4 a c 2 a . Theorem used: “If r 1 = α + i β and r 1 = α − i β are the two complex roots of the auxiliary equation a r 2 + b r + c = 0 , then y = e α x ( c 1 cos β x + c 2 sin β x ) is the general solution of a y ″ + b y ′ + c y = 0 . The general solution y = y ( x ) to the nonhomogeneous differential equation a y ″ + b y ′ + c y = G ( x ) has the form y = y c + y p , where the complementary solution y c is the general solution to the associated homogeneous equation a y ″ + b y ′ + c y = 0 , and y p is any particular solution to the nonhomogeneous equation a y ″ + b y ′ + c y = G ( x ) ”. Calculation: The voltage source is: E = 0 The resistance R is 0 Ω , the capacitance C is 50 nF , and the inductance L is 2 mH . Now, the governing equation of Kirchhoff’s law is: L q ″ + R q ′ + 1 C q = E ( t ) Where, q is the charge at a cross section of a conductor, measured in coulombs, I is the current or rate of change d q d t (flow of electrons) at a cross section of a conductor, measured in amperes, E is the electric (potential) source, measured in volts, and V is the difference in potential between two points along the conductor, measured in volts ( v ). Substitute the resistance R is 0 Ω , the capacitance C is 50 nF , and the inductance L is 2 mH . in L q ″ + R q ′ + 1 C q = E ( t ) . 2 × 10 − 3 d 2 q d t 2 + 0 d q d t + 1 50 × 10 − 9 q = 0 2 10 3 d 2 q d t 2 + 10 9 50 q = 0 The auxiliary equation is: 2 10 3 m 2 +

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Author: Allyn Washington, Richard Evans

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Chapter 31.10, Problem 18E

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Chapter 31 Solutions

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

Ch. 31.1 - Show that is a solution of . Is it the general...Ch. 31.1 - Prob. 1E Ch. 31.1 - In Exercises 1 and 2, show that the indicated...Ch. 31.1 - In Exercises 3–6, determine whether the given...Ch. 31.1 - Prob. 4E Ch. 31.1 - In Exercises 3–6, determine whether the given...Ch. 31.1 - Prob. 6E Ch. 31.1 - In Exercises 7–10, show that each function y =...Ch. 31.1 - Prob. 8E Ch. 31.1 - In Exercises 7–10, show that each function y =...

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