Explanation Given data: Refer to Figure given in the textbook. The value of the inductor is L = 160 mH . The value of the resistor is R = 8 k Ω The value of the capacitor is C = 10 nF The value of the voltage source is 50 V. Formula used: Write the general expression for resonant radian frequency as follows, ω 0 = 1 L C (1) Write the general expression for neper frequency as follows, α = R 2 L (2) Write the general expression for damping frequency as follows, ω d = ω 0 2 − α 2 (3) Write the general expression for current through the inductor as follows, i L ( t ) = L d v o ( t ) d t (4) Calculation: The circuit has been in operation for a long time under steady state. Therefore, the capacitor acts as an open circuit and inductor behaves like a short circuit. The modified circuit is shown in Figure 1. Therefore, the initial current through the inductor and the initial voltage across the capacitor are, i L ( 0 ) = 0 A v o ( 0 ) = 50 V i C ( 0 ) = 0 A Consider the given circuit shown in Figure 2 for t > 0 . Substitute 8 k for R and 160 m for L in equation (2) as follows, α = 8 × 10 3 2 ( 160 × 10 − 3 ) { ∵ 1 k = 10 3 , 1 m = − 10 − 3 } = 25000 rad s Squaring the above equation as follows, α 2 = 625 × 10 6 rad s Substitute 160 m for L and 10 n for C in equation (1) as follows, ω 0 2 = 1 ( 160 × 10 − 3 ) ( 10 × 10 − 9 ) { ∵ 1 n = 10 − 9 , 1 m = − 10 − 3 } = 625 × 10 6 rad s As α 2 = ω 0 2 , the output response is critically damped. Hence, the output equation will be as follows, v o ( t ) = V f + D 1 t e − α t + D 2 e − α t (5) In Figure 2, the value of V f is, V f = 250 V Substitute 250 for V f and 25000 for α in equation (5) as follows, v o ( t ) = 250 + D 1 t e − 25000 t + D 2 e − 25000 t (6) Substitute 0 for t in equation (6) as follows, v o ( 0 ) = 250 + D 1 ( 0 ) e − 25000 ( 0 ) + D 2 e − 25000 ( 0 ) v o ( 0 ) = 250 + D 2 { ∵ e 0 = 1 }

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Chapter 8, Problem 49P

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2. With respect to the circuit shown in Figure 2 below V2 -R1 R2 R4 w R3 R5 Figure 2: DC Circuit 2 a. Using Ohm's and Kirchhoff's laws calculate the current flowing through R3 and so determine wattage rating of R3. b. Verify your results with simulations. Note: you must use the values for the components in Table 2. Table 2 V2 (Volts) R1 (KQ) R2 (KQ) R3 (KQ) R4 (KQ) R5 (KQ) 9 3.3 5 10 6 1 3.3

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Chapter 8 Solutions

Electric Circuits. (11th Edition)

Ch. 8.1 - The resistance and inductance of the circuit in...Ch. 8.2 - Use the integral relationship between iL and v to...Ch. 8.2 - Prob. 3AP Ch. 8.2 - Prob. 4AP Ch. 8.2 - Prob. 5AP Ch. 8.3 - Prob. 6AP Ch. 8.4 - Prob. 7AP Ch. 8.4 - Prob. 8AP Ch. 8.4 - Repeat Assessment Problems 8.7 and 8.8 if the 80 Ω...Ch. 8 - The resistance, inductance, and capacitance in a...

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02 - Sinusoidal AC Voltage Sources in Circuits, Part 1; Author: Math and Science;https://www.youtube.com/watch?v=8zMiIHVMfaw;License: Standard Youtube License

Find the expression for the voltage v o ( t ) for t ≥ 0 .

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Chapter 8 Solutions