+1 + R VR ĪR + + L V Vs I. IL Consider the RLC circuit shown. The sinusoidal voltage source has a magnitude of IV 1. Answer the following questions, showing your solutions where applicable. a. Find an expression for the complex gain, |A| (1) b. Derive an expression for the cutoff frequency/ies of the circuit. (Hint: The cutoff frequency, w, is the frequency at which the output voltage is of the input voltage.) √2 c. What is the expected behavior of the output as the frequency approaches ∞? When the frequency approaches 0? d. At what frequency will the voltage gain be at a maximum? C

+1 + R VR ĪR + + L V Vs I. IL Consider the RLC circuit shown. The sinusoidal voltage source has a magnitude of IV 1. Answer the following questions, showing your solutions where applicable. a. Find an expression for the complex gain, |A| (1) b. Derive an expression for the cutoff frequency/ies of the circuit. (Hint: The cutoff frequency, w, is the frequency at which the output voltage is of the input voltage.) √2 c. What is the expected behavior of the output as the frequency approaches ∞? When the frequency approaches 0? d. At what frequency will the voltage gain be at a maximum? C

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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a. In an RC circuit supplied with AC power, a 500 ohm resistor is used to create a system with a crossover frequency wc =440 rad/s. What capacitance is the capacitor in this circuit? b. If an inductor is to be added to this circuit to make the resonant frequency equal to the crossover frequency, then what inductance must this inductor have? c. If, near a particular time t1, the instantaneous voltage drop over the resistor is given by v(t1)=0.65V cos(440t), then what is i(t1) (the function of instantaneous current with respect to time) for its capacitor? d. What would the Irms value be based on the sinusoidal function you found in part c? (Pick off Ipeak from the function, then plug in to rms equation) Since this is multi-part, answers to later parts will be graded based on your answers to previous parts when necessary.
a) In an RC circuit supplied with AC power, a 500 ohm resistor is used to create a system with a crossover frequency wc =440 rad/s. What capacitance is the capacitor in this circuit? b. If an inductor is to be added to this circuit to make the resonant frequency equal to the crossover frequency, then what inductance must this inductor have? c. If, near a particular time t1, the instantaneous voltage drop over the resistor is given by v(t1)=0.65V cos(440t), then what is i(t1) (the function of instantaneous current with respect to time) for its capacitor? d. What would the Irms value be based on the sinusoidal function you found in part c? (Pick off Ipeak from the function, then plug in to rms equation)
Given the RLC circuit below and given that the sinusoidal voltage source has a magnitude of |Vs|, do the following: Find an expression for the complex gain (|Aω| = Vo / Vs) Derive an expression for the cutoff frequencies of the circuit (Note: The cutoff frequency is the frequency at which the output voltage is roughly 1/√2 of the input voltage) What is the expected behavior of the circuit as the frequency approaches infinity? What about when the frequency is 0? Finally, what is the frequency in which the voltage gain will be at maximum? Explain why.
In the circuit in the figure, Vcc= 18 V, Rs1 = 0.9 k2, Rs2 = 0.5 kQ, R1 = 75 kQ, R2 = 15 kQ, RC = 2.2 kQ, RE = 1 k and B = 120. It is also known that Cwi = 6 pF, Cwo = 10 pF, Cbc = Cu = 7 pF, Cbe = C = 44 pF and Cce = 11 PF. Accordingly, considering the frequency response of the circuit, what would the high cutoff frequency (fH) be? NOTE-1: The output impedance of the transistor is ro = 20 k and will be taken into account in the calculations. NOTE-2: high frequency dependence of hfe, B. will be taken into account.
Perhaps surprisingly, we can apply the transfer-function concept to mechanical systems. Suppose we have a mass m moving through a liquid with an applied force f and velocity v. The motion of the mass is described by the first-order differential equationf=m dv dt +kv in which k is the coefficient of viscous friction. Find an expression for the transfer functionH( f )= V F Also, find the half-power frequency (defined as the frequency at which the transfer function magnitude is 1/2 times its dc value) in terms of k and m.
Starting with the differential equation of an RL circuit, calculate:(a) The frequency response of system (G(f) = G(s)|s=j2πf ). Considerthe input to be the applied voltage Vs(t) and the output to be thethe voltage across the inductor VL(t)).(b) For R = L = 1, Calculate and sketch the magnitude of the frequencyresponse |G(f)|. Show explicitly the magnitude values for f = 0, f =1f = ∞.(c) For R = L = 1, Calculate and sketch the phase of the frequencyresponse ∠ {G(f)}. Show explicitly the magnitude values for f =0, f = 1f = ∞.
A second order system with a natural frequency (wn) of 6 rad/sec and damping ratio of x = 0.5, the value of maximum overshoot is equal to?
100 y(t)+ y (t) = X(t) for a system defined by a first-order differential equation:a. Draw the log magnitude(dB)-log frequency graph of H (jw) (phase graph is not requested. it is expected that the frequency axis will also be logarithmic when plotting the log magnitude graph).b. If the magnitude of H(jw) is -40 dB, it is assumed that the input is suppressed. it is given that the signal X (t) = coswat is suppressed by this system. What is the smallest wa value in this case?
1)The circuit shown below is initially, for t < 0, with capacitor C connected to a battery (Vbat = 12 V). The key is switched at t = 0, disconnecting the battery and turning on the capacitor to the rest of the circuit.a) Determine the energy stored in the circuit at t = 0 . b) Draw an equivalent circuit for the frequency domain, valid for t ≥ 0. Indicate the values of all components of the equivalent circuit.c) Determine the expression for the loop current in the frequency domain, I(s), expanded into partial fractions.
The network as shown has two poles. (a) Estimate the lower-pole frequency using the shortcircuit time-constant technique if C1 = 1 μF, C2 = 10 μF, R1 = 10 kΩ, R2 = 1 kΩ, and R3 = 1 kΩ. (b) Estimate the upper-pole frequency. (c) Why do the positions of the poles seem to be backward? (d) Find the system determinant and compare its exact roots to those in (a) and (b).
A second order system with a natural frequency (wn) of 6 rad/sec and damping ratio of 0.5, the value of rise time?
For the following system: G (s) = 15 / ( 10s + 11) Assume input u(t) = 10 Find the values of: -Damping factor -Natural Frequency -Damped Natural Frequency