Question

Please solve the questions for the following problems.
a. In an overdamped natural response, S1=200 rad/sec, S2=3000rad/sec, v(0)=20v, and dv(0)/dt = 10v/sec. Determine the voltage equation v(t) .
b. For a given series RLC circuit, R=632?, L=100mH, and C=1.001uF. Determine what kind of damping is the circuit.
c. How do you determine if a circuit is overdamped? There may be multiple answers so give a specific answer as it applies to RLC circuits.
d. Is a critically damped circuit practical to build? Why or Why not?
e. S1 and S2 are for an underdamped circuit. What type of values or numbers are S1 and S2?

2. The following questions pertain to questions about phasor analysis where a standard US
outlet operates at 125Vrms at 60Hz.
a. Describe in one or two words the shape of the waveform of the current flowing through an appliance in your house.
b. What is the frequency of the voltage at an outlet in rads/sec.
c. What is the peak amplitude of the voltage at an outlet?
d. A toaster can be modeled as a resistor and inductor. Will the total complex impedance of the toaster have a positive or negative angle?
e. For the toaster in the previous question, will voltage across the toaster lead or lag the current through the toaster?

please help me answering all these questions as fast as possaible

Answer 1

e. A circuit to be under-damped ,the roots of CE equation mentioned in part( a ) must be complex in nature. Hence S1 and S2 will be a complex poles incase of under-damped system.