Question

1. A paralll RLC circuit consists of a A series RLC circuit consists of the same 5000 Ω resistor, 1.25 H inductor, and 8 nF capacitor. a) Find the roots of the characteristic 2. 5000 Ω resistor, a 1.25 H inductor, and an 8 nF capacitor. a) Find the roots of the characteristic equation equation b) Is the response over-damped or b) Is the response over-damped or under-damped? under-damped? c) How would you need to change the resistance to get the other form of damping? c) How would you need to change the resistance to get the other form of damping?

Answer 1

Apply Laplace transform 1/Z = 1/5000 + 1/1.255 + 1/115 times 10^6/5 1/Z = 25000s + 10^8 + s^2/125 times 10^6 times 5 Z = 125 times 10^6 times s/s^2 + 25000s + 10^8 Characteristic equation is s^2 + 25000s + 10^8 = 0 s_1 = -5000, s_2 = -20000 compare characteristic eqn with s^2 + 2 omega n + omega n^2 = 0 omega n^2 = 10^8 = > omega n = 10^4 rad/sec z omega n = 25000 = 1.25 > 1 over damped system IL R = 6250 ohm = 1/2R squareroot L/C Then system is critically damped. If R > 6250, under damped If R = infinity ohm, undamped \r\n characteristic equation is 5000 + 1.255 + 125 times 10^6/5 = 0 1.25 s^2 + 5000s + 125 times 10^6 = 0 s^2 + 4000s + 10^8 = 0 s_1,2 = -2000 plusminus j 9797.959 compare characteristic equation with s^2 + 2 omega n s + omega^2_n

According to HomeworkLib guide lines we will solve 4 sub questions in a given problem.

If you have any doubt please make a comment. Thank you