Q3) Consider the following RLC circuit, where the input voltage is V (L) and the se voltage of the capacitor V.(t). ilt)

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Q3 Consider The Following Rlc Circuit Where The Input Voltage Is V L And The Se Voltage Of The Capacitor V T Ilt 1 (67.48 KiB) Viewed 63 times

Q3) Consider the following RLC circuit, where the input voltage is V (L) and the se voltage of the capacitor V.(t). ilt) R. m m C I.lt) vit) a) Assume zero initial conditions, show that the transfer function is given by /c s2 + Rs/L+/c where 7(s) = G(s)/(s) G(s) b) [4 Marks) Derive the undamped natural frequency, damping ratio and the steady state gain in terms of the system components. [4 Marks] If R = 280N and V(t) is a unit step, find the values of L and C that yield a response with 40% overshoot and a settling time of 0.0029 second. What are the poles of this system? c) [8 Marks] d) Specify a condition for the component values R and L that yield sustained oscillation. What will be the frequency of this oscillation? Hence, specify the pole location in terms of the component values. [4 Marks)