question 1 given the series rlc resonant circuit

Question

Question 1: Given the series RLC resonant circuit in the figure, operating at variable frequency, determine: 

a. The resonant frequency ω_o 

b. The circuit’s quality factor Q 

c. The cut-off frequencies, f₁ & f₂ and the bandwidth BW 

d. The maximum peak current I_max 

e. The maximum power and the cut-off power values

 

Question 2) : For the circuit given in problem # 1, determine: 

a. The differential equation describing the total current in the circuit 

b. Sketch the frequency-domain (s-domain) equivalent circuit 

c. Using the LaPlace transform, determine the s-domain current in the circuit 

d. Solve the differential equation for the time-domain current 

e. Applying the inverse LaPlace transform determine the time-domain current, and compare with 

the solution in “d”. 

Question 3: For the parallel RLC resonant circuit in the figure, operating at variable frequency, determine: 

a. The resonant frequency ωo 

b. The circuit’s quality factor Q 

c. The cut-off frequencies, f1 & f2 and the bandwidth BW 

d. The maximum peak current Imax

e. The maximum power and the cut-off power values

Qi\uestion 4: Given the circuit in problem # 3, determine: 

a. The differential equation describing the total voltage of the circuit (nodal voltage) 

b. Sketch the frequency-domain (s-domain) equivalent circuit 

c. Using the LaPlace transform, determine the s-domain nodal voltage of the circuit 

d. Solve the differential equation for the time-domain nodal voltage 

e. Applying the inverse LaPlace transform determine the time-domain nodal voltage, and compare 

with the solution in “d”.