Question

1. In the circuit shown in Fig. 1, where L-8 mH and R-8 kQ, a Determine how the input impedance Z(ja)= behaves at extremely high and low frequencies. b. Find an expression for the impedance. c. Show that this expression can be manipulated into the form Zjo) RI+ d. Determine the frequency-o for which the imaginary part of the expression in part c is equal to 1. e. Estimate (without computing it) the magnitude and phase angle of Zö o) at ω= 105 rad's, 106 rad/s, and 107 rad/s. (Jw) Fig. 1

Answer 1

PLEASE FIND THE SOLUTION FOR ABOVE QUESTION WITH ITS RESPECTIVE SUB POINTS
Given rightarrow L = 8mH: R = 8 K Ohm a) to find V_i (jw)/I_1 (jw) = ? by applying KVL equation in loop 1 V_i (t) + i R + Ldi_1 (t)/dt rightarrow 1 equation by applying laplace transformation in equation 1 to obtain frequency domain analysis and impedance transfer function laplace x(t) rightarrow^alpha X(s) where general laplace rightarrow X(s) = integral^infinity_+ infinity x(t) e^- st dt so equivalent terms in eqn 1 will become V_i (t) rightarrow V_i (s) rightarrow val 1 i_i (t) rightarrow I_i (s) rightarrow val 2 laplace of differential term will be given as } rightarrow Ldi(t)/dt rightarrow LS I: (s) - Li (0^-) rightarrow val 3 rightarrow from initial condition by assuming zero initial condition i(0^-) = 0 and substituting values ie val 1, val 2, val 3 in eq^n 1 we get V_I (s) = RI_i (s) + LSI_i (s) rightarrow equation 2 V_I (s) = [R + LS] I_i (s) V_I(s)/I_i (s) = R + LS \r\n by putting S = jw in eq^n 2

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