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2. A 10 mH inductor, a 1 μF capacitor, and a variable resistor are connected in parallel in the circuits shown. The resistor is adjusted so the roots of the characteristic equation are -8000+ j6000 rad/s. The initial voltage on the capacitor is 10 V and in the initial current in the inductor is 80 mA. Find a. The damped form of the response b. R dv(0+) c. ic + iL iR dt d. v(t) e. iL(t) Vo L R - w 2. a. Underdamped (the roots are complex) b. R 62.5 Q dv(0+) C. dt =-240,000 V/s 80 d. vc(t) = e-8000t [10cos (6000t) - 30 sin (6000t)] V 820 e. (t) = e-8000t 80 cos(6000t) +1 3 sin(6000t)] mA i(t) = e-8000t [.08 cos(6000t) + 41 150 sin (6000t)] A + ข

2. A 10 mH inductor, a 1 μF capacitor, and a variable resistor are connected in parallel in the circuits shown. The resistor is adjusted so the roots of the characteristic equation are -8000+ j6000 rad/s. The initial voltage on the capacitor is 10 V and in the initial current in the inductor is 80 mA. Find a. The damped form of the response b. R dv(0+) c. ic + iL iR dt d. v(t) e. iL(t) Vo L R - w 2. a. Underdamped (the roots are complex) b. R 62.5 Q dv(0+) C. dt =-240,000 V/s 80 d. vc(t) = e-8000t [10cos (6000t) - 30 sin (6000t)] V 820 e. (t) = e-8000t 80 cos(6000t) +1 3 sin(6000t)] mA i(t) = e-8000t [.08 cos(6000t) + 41 150 sin (6000t)] A + ข

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Trying to understand for learning purposes the steps to find a ~ e.  Could you please explain/show how this is derived?

2. A 10 mH inductor, a 1 μF capacitor, and a variable resistor are connected in parallel in the circuits shown. The resistor is adjusted so the roots of the characteristic equation are -8000+ j6000 rad/s. The initial voltage on the capacitor is 10 V and in the initial current in the inductor is 80 mA. Find a. The damped form of the response b. R dv(0+) c. ic + iL iR dt d. v(t) e. iL(t) Vo L R - w 2. a. Underdamped (the roots are complex) b. R 62.5 Q dv(0+) C. dt =-240,000 V/s 80 d. vc(t) = e-8000t [10cos (6000t) - 30 sin (6000t)] V 820 e. (t) = e-8000t 80 cos(6000t) +1 3 sin(6000t)] mA i(t) = e-8000t [.08 cos(6000t) + 41 150 sin (6000t)] A + ข
Transcribed Image Text:2. A 10 mH inductor, a 1 μF capacitor, and a variable resistor are connected in parallel in the circuits shown. The resistor is adjusted so the roots of the characteristic equation are -8000+ j6000 rad/s. The initial voltage on the capacitor is 10 V and in the initial current in the inductor is 80 mA. Find a. The damped form of the response b. R dv(0+) c. ic + iL iR dt d. v(t) e. iL(t) Vo L R - w 2. a. Underdamped (the roots are complex) b. R 62.5 Q dv(0+) C. dt =-240,000 V/s 80 d. vc(t) = e-8000t [10cos (6000t) - 30 sin (6000t)] V 820 e. (t) = e-8000t 80 cos(6000t) +1 3 sin(6000t)] mA i(t) = e-8000t [.08 cos(6000t) + 41 150 sin (6000t)] A + ข
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