Questions and Answers of Schaum S Outline Of Electric Circuits

A two-element series circuit, with R = 10 Ω and L = 20 mH, has current i = 5 sin 100t + 3 sin 300t + 2 sin 500t (A) Find the effective applied voltage and the average power.
A pure inductance, L = 10 mH, has the triangular current wave shown in Fig. 17-59, where w = 500 rad/s. Obtain the exponential Fourier series for the voltage across the inductance. Compare the answer
A three-element series circuit, with R = 5 Ω, L = 5 mH, and C = 50 μF, has an applied voltage u = 150 sin 1000t + 100 sin 2000t + 75 sin 3000t (V). Find the effective current and the average power
Figure 17-61 shows a full-wave-rectified sine wave representing the voltage applied to the terminals of an LC series circuit. Use the trigonometric Fourier series to find the voltages across the
A pure inductance, L = 10 mH, has an applied voltage with the waveform shown in Fig. 17-60, where ω = 200 rad/s. Obtain the current series in trigonometric form and identify the current waveform.
A three-element circuit consists of R = 5 Ω in series with a parallel combination of L and C. At ω = 500 rad/s, XL = 2 Ω, XC = 8 Ω . Find the total current if the applied voltage is given by v =
Obtain the voltage transfer function Hv∞ for the open circuit shown in Fig. 12-11. At what frequency, in hertz, does |Hv |= 1/√2 if(a) C2 = 10 nF,(b) C2 = 1 nF? V₁ R₁ = 5 kn www 1₂ = 0
A simple voltage divider would consist of R1 and R2. If stray capacitance Cs is present, then the divider would generally be frequency-dependent. Show, however, that V2/V1 is independent of frequency
Find the poles and zeros of H(s) = 10s/(s2 + 2s + 26). Place them in the s-domain and use the pole-zero plot to sketch H(jw).
Find the frequency at which |Hv| = 0.50 for the low-pass RC network shown in Fig. 12-42.Data from figure 12-42 R₁ = 100 www C₂=2 μF
Assume that a sinusoidal voltage source with a variable frequency and Vmax = 50 V is applied to the circuit shown in Fig. 12-59.(a) At what frequency f is |I| a minimum?(b) Calculate this minimum
Three network functions H1, H2, and H3 are given:(a)(b)(c)Find the magnitude of their frequency responses. Show that all three functions are lowpass with half power frequency at ωc = 1. H₁= 1 s+1
For the series RLC circuit shown in Fig. 12-43, find the resonant frequency ω0 = 2πf0. Also obtain the half-power frequencies and the bandwidth β. V(w) 100 Ω 0.5 H 0.4 μF
A 20-µF capacitor is in parallel with a practical inductor represented by L = 1 MHz in series with R = 7 Ω. Find the resonant frequency, in rad/s and in Hz, of the parallel circuit.
Find the network function V2/V1 in the circuits shown in(a) Fig. 12-16 (a) and(b) Fig. 12-16(b). + V₁ www R = 10 L=1/√2H C=V2F V₂ V₁0-M √2/202 A √2/202 1 F V₂ B 2 F He
Derive the Q of(a) The series RLC circuit,(b) The parallel RLC circuit.
What must be the relationship between the values of RL and RC if the network shown in Fig. 12-60 is to be resonant at all frequencies? RL 2 mH Rc 80 µF
Consider the network function H(s) = 10s/(s2 + 300s + 106). Find the center frequency, the lower and upper half-power frequencies, the bandwidth, and the quality factor.
A three-element series circuit contains R = 10 Ω, L = 5 mH, and C = 12.5 μF. Plot the magnitude and angle of Z as functions of ω for values of ω from 0.8 ω0 through 1.2 ω0.
For the parallel network shown in Fig. 12-61,(a) Find the value of R for resonance;(b) Convert the RC branch to a parallel equivalent. 10 Ω j10 Ω R 5-2 Ω
Repeat Example 12.7 for H(s) = 10s/(s2 + 30s + 106).Data from Example 12.7Consider the network function H(s) = 10s/(s2 + 300s + 106). Find the center frequency, the lower and upper half-power
For the network of Fig. 12-62(a), find R needed for resonance. Obtain the values of R′, XL, and XC in the parallel equivalent of Fig. 12-62(b). R j10 Ω (α) 10 Ω -j5 Ω R' (b) jX₁ -jXc
A parallel RC circuit has the Y- and Z-loci shown in Fig. 12-29; these are derived from Y 1/2 + jac R and R √1 + (@CR)² 2=J tan (-@CR)
A coil is represented by a series combination of L = 50 mH and R = 15 Ω. Calculate the quality factor at(a) 10 kHz,(b) 50 kHz.
Branch 1 of a two-branch parallel circuit has an impedance Z1 = 8 + j6 Ω at w = 5000 rad/s. Branch 2 contains R = 8.34 Ω in series with a variable capacitance C. (a) Find C for
For the RLC series circuit, the Y-locus, with ω as the variable, may be determined by writing whence Y = G+ jB= G = R R² + X² R+ jX B = R-jX R² + X² X R² + X²
Determine the value(s) of L for which the circuit shown in Fig. 12-68 is resonant at 5000 rad/s. 2 Ո 5 2 20 F
In the circuit of Fig. 12-47, let R1 = R2 = 2 kΩ, L = 10 mH, and C = 40 nF. Find the resonant frequency and bandwidth, and compare with the results for R1 = 0 (i.e., a pure parallel circuit).
The RC circuit shown in Fig. 12-33 (b) is a non-inverting lowpass filter. With R = 1 kΩ and C = 1 mF, its network function and frequency response are H₂ (s) = 1000 s +1000 H₂ (jw) = 1 1+
(a) Construct the admittance locus diagram for the circuit shown in Fig. 12-66.(b) For what value of resistance in the RL branch is resonance possible for only one value of XL? 10 Ω jXL 5 Ω -j10
Obtain the bandwidth β for the circuit of Fig. 12-47 and plot β against the parameter R = X R.R₂ R₁ + R₂
A leaky integrator is made up of an inverting op amp with a parallel RfC circuit in the feedback path and R1 in the input. See Fig. 12-33(a), with R1 = Rf = 1 kΩ and C = 1 mF. The network function
Convert the circuit constants of Problem 12.10 to the parallel form. Calculate the quality factor at(a) At 10 kHz,(b) At 250 Hz.Data from Problem 12.10A coil is represented by a series combination
In Problem 12.32, for what values of the inductive reactance will it be possible to obtain resonance at some value of the variable resistance R?Data from Problem 12.32Find R for resonance of the
For the circuit shown in Fig. 12-47,(a) Obtain the voltage transfer function Hv(ω) and(b) Find the frequency at which the function is real. M R₁ R₂ www F V₂
For the practical “tank” circuit examined in Section 12.14, theData from Figure 12-32 Y-locus may be constructed by combining the C-branch locus and the RL-branch locus. To illustrate the
Find R for resonance of the network shown in Fig. 12-64. Sketch the admittance locus diagram. 4 Ω -j5 Ω (2) R j10 Ω
Plot the frequency response of the network function H(s) = l/(s + 1) in the form of a Bode diagram for 0.01 < ω < 100 rad/s.
A three-branch parallel circuit has fixed elements in two branches; in the third branch, one element is variable. The voltage -current phasor diagram is shown in Fig. 12-69. Identify all the elements
Plot the magnitude response of normalized lowpass Butterworth filters for n = 1,…,10. Discuss the effect of increasing n on the aecuracy of the approximation.
In the circuit of Fig. 12-72, Z1 = R + 1/(Cs) and Z2 = R, with RC = 0.5 ms and A = ∞ (an ideal op amp).(a) Find the frequency response H (jω) =V2/V1 .(b) Determine the order and type of the
Plot the frequency response of the transfer function H(s) = s/(s + 1) in the form of a Bode diagram for 0.01 < ω < 100 rad/s.
Measurements on a practical inductor at 10 MHz give L = 8.0 µH and Qind = 40.(a) Find the ideal capacitance C for parallel resonance at 10 MHz and calculate the corresponding bandwidth
In the circuit of Fig. 12-71, L = 1 mH. Determine R1, R2, and C such that the impedance between the two terminals of the circuit is 100 Ω at all frequencies. Z- R₁ L = 1 mH R₂
Compare the resonant frequency of the circuit shown in Fig. 12-50 for R = 0 to that for R = 50 Ω. 30 μF R 0.2 H
Describe the circuit which corresponds to each locus in Fig. 12-70 if there is only one variable element in each circuit. Locus of IT (a) (b) Locus of Ir (c) Locus of IT
For the circuit of Fig. 12-47, R1 = 5 kΩ and C = 10 nF. If V2/V1 = 0.8 ∠ 0° at 15 kHz, calculate R2, L, and the bandwidth. V₁ R₁ R₂ V: Œ L
A lossy capacitor, in the series-circuit model, consists of R = 25 Ω and C = 20 pF. Obtain the equivalent parallel model at 50 kHz.
A variable-frequency source of V = 100 ∠ 0° V is applied to a series RL circuit having R = 20 Ω and L = 10 mH. Compute I for ω = 0, 500, 1000, 2000, 5000 rad/s. Plot all currents on the same
Repeat Problem 12.39 for the circuit of Fig. 12-73.Data from Problem 12.39In the circuit of Fig. 12-72, Z1 = R + 1/(Cs) and Z2 = R, with RC = 0.5 ms and A = ∞ (an ideal op amp).(a) Find the
The network function of the circuit of Fig. 8-42 with R = 2 kΩ, C = 10 nF, and R2 = R1 is H(s) = V. 1 2 S S (GJÏ·G·· + || +1
The circuit shown in Fig. 12-53 is in resonance for two values of C when the frequency of the driving voltage is 5000 rad/s. Find these two values of C and construct the admittance locus diagram
In the circuit of Fig. 12-72,at 5 Hz).(a) Find the frequency response H j(ω) = V2/V1.(b) Determine the order and type of the filter.(c) Specify asymptotic magnitude (dB) and phase (degree) at low
A voltage source is connected to the terminals of a series RLC circuit. The phasor current is I = Y × V, where Y(s) = Cs LCs² + RCs +1
Given H(s) = s/(s2 + as + b), determine a and b such that the magnitude of the frequency response |H( jω)| has a maximum at 100 Hz with a half-power bandwidth of 5 Hz. Then find the quality factor Q.
In the circuit of Fig. 12-72,with a0 = 2 × 105 and ω0 = 10π. Find the frequency response H(ω) =V2/V1 and compare it with the frequency response of the circuit under an ideal op amp assumption
In the circuit of Fig. 12-72, assume R = 1 kΩ, C = 100 nF, and A = ∞. For each entry given in the following table, derive and verify the listed H( jω) and the magnitude Bode plot. Show that in
Repeat Problem 12.41 for the circuit of Fig. 12-73.Data from Problem 12.41In the circuit of Fig. 12-72,at 5 Hz).(a) Find the frequency response H j(ω) = V2/V1.(b) Determine the order and type of
Show by locus diagrams that the magnitude of the voltage between points A and B in Fig. 12-55 is always one-half the magnitude of the applied voltage V as L is varied. V R R M N 1₂ (2) B R₁
In the circuit of Fig. 7-45 (a) let RC = 5 × 10−7 s. Find the transfer function H(s) =V2/V1 and the magnitude and phase of the frequency response. Specify the order and type of the filter.
Given V2/V1 = 10s/(s2 + 2s + 81) and v1(t) = cos (ωt), determine ω such that the amplitude of v2(t) attains a maximum. Find that maximum.
In the circuit of Fig. 12-74(b), let R = 1 Ω, C1 = 1.394 F, C2 = 0.202 F, and C3 = 3.551 F. Find H(s) = V2/V1 and show that it approximates the passive third-order Butterworth low-pass filter of
The coil of Problem 12.50 placed in parallel with a capacitor C resonates at 600 kHz. Find C, quality factor Q, and bandwidth Δf in kHz.Data from Problem 12.50A coil is modeled as a 50-μH inductor
A coil is modeled as a 50-μH inductor in series with a 5-Ω resistor. Specify the value of a capacitor to be placed in series with the coil so that the circuit would resonate at 600 kHz. Find the
Given H(s) = (s + 1)/(s2 + 2s + 82), determine where |H( jω)| is at a maximum, its half-power bandwidth and quality factor.
In a parallel RLC circuit, R = 10 kΩ and L = 20 μH.(a) Find C so that the circuit resonates at 1 MHz. Find the quality factor Q and the bandwidth in kHz.(b) Find the terminal voltage of the
Plot the magnitude and phase of the frequency response of a circuit with the transfer function for Q = 0.2, 0.5, 0.707, 5, 10, 20, and 50. 1 H(s) = 1/( 3² + √ √5 + 1) s
Plot the magnitude and phase of the frequency response of normalized n-th order lowpass Butterworth filters.
Find RLC values in the low-pass filter of Fig. 12-74(a) to move its half-power cutoff frequency to 5 kHz. 2/1 V/1 www 192 1F (a) ell 2 H IF 192 2/₂
Show that the half-power cutoff frequency in the circuit of Fig. 8-42 is ω0 = 1/(RC) and, therefore, frequency scaling may be done by changing the value of C or R.
(a) Find the transfer function H(s) = V2/V1 for the filter of Fig. 12-77 (a) and determine its type.(b) Assuming R = 159 Ω, C = 1 µF, and b ≡ R1/(R1 + R2), find the notch frequency and plot
The circuit in Fig. 12-74 (a) is a third-order Butterworth low-pass filter. Find the network function, the magnitude of the frequency response, and the half-power cutoff frequency ω0.
In a first-order, lowpass Butterworth filter with fc = 1000 Hz, find the attenuation (in dB) ata) 50 Hz,b) 500 Hz,c) 1 kHz,d) 5 kHz, ande) 10 kHz.
Evaluate the magnitude response of the nth order, normalized lowpass Butterworth filter at ω = 1/2 and 2 for n = 1 through 10. Show that as n goes from 1 to 10, the magnitude approaches that of the
Find the attenuation (in dB) of the lowpass filter with ata) 5 Hz,b) 10 Hz, andc) 20 Hz. 1 2 s² + 20n√2s+ 400m² H(s) = 2
Find the order of a lowpass Butterworth filter such that the attenuation at 1180 Hz is 0.5 dB and at 10 kHz is 28 dB.
Using the method of lowpass-to-highpass transformation, determine H(s) for a second-order, highpass Butterworth filter with fc = 1 kHz.
Two balanced Δ-connected loads, with impedances 20 ∠ −60° Ω and 18 ∠ 45°, respectively, are connected to a three-phase system for which a line voltage is VBC = 212.1 ∠ 0° V. Obtain the
A balanced Δ-connected load, with ZΔ = 30∠30° Ω, is connected to a three-phase, three-wire, 250-V system by conductors having impedances Zc = 0.4 + j0.3 Ω. Obtain the line-to-line voltage at
In Problem 11.5, a balanced Δ-connected load with Z = 20 ∠ 45° Ω resulted in line currents 8.65 A for line voltages 100 V, both maximum values. Find the readings of two wattmeters used to
Obtain the readings of two wattmeters in a three-phase, three-wire system having effective line voltage 240 V and balanced, Δ-connected load impedances 20 ∠ 80° Ω.
A three-phase, three-wire, ABC system, with line voltage VBC = 311.1 ∠0° V, has line currentsFind the readings of wattmeters in lines(a) A and B,(b) B and C, and(c) A and C. IA = 61.5
A three-phase, three-wire, ABC system has an effective line voltage 440 V. The line currents areObtain the readings of wattmeters in lines(a) A and B,(b) B and C. = 27.9/90° A IA= I = 81.0-9.9°
(a) Find L2 in the high-pass circuit shown in Fig. 12-41, if |Hv(ω)| = 0.50 at a frequency of 50 MHz.(b) At what frequency is |Hv| = 0.90?Data from Figure 12-41 R = 50 kn Vi T L₂ Vz
Two wattmeters in a three-phase, three-wire system with effective line voltage 120 V read 1500 W and 500 W. What is the impedance of the balanced Δ-connected load?
A three-phase, three-wire, ABC system has effective line voltage 173.2 V. Wattmeters in lines A and B read −301 W and 1327 W, respectively. Find the impedance of the balanced Y-connected load.
A three-phase, three-wire system, with a line voltage VBC = 339.40° V, has a balanced Y-connected load of ZY = 15 ∠ 60° Ω. The lines between the system and the load have impedances 2.24 ∠
Repeat Problem 11.39 with the load impedance ZY = 15 ∠ −60° Ω. By drawing the voltage phasor diagrams for the two cases, illustrate the effect of the load impedance angle on the voltage drop
A three-phase generator with an effective line voltage of 6000 V supplies the following four balanced loads in parallel: 16 kW at pf = 0.8 lagging, 24 kW at pf = 0.6 lagging, 4 kW at pf = 1, and 1 kW
A balanced Δ-connected load with impedances ZΔ = 6 + j9 Ω is connected to a three-phase generator with an effective line voltage of 400 V. The lines between the load and the generator have
A three-phase, three-wire source supplies a balanced load rated for 15 kW with pf = 0.8 at an effective line voltage of 220 V. Find the power absorbed by the load if the three wires connecting the
In Problem 11.47 determine the effective value of the line voltage such that the load operates at its rated values.Data from problem 11.47A three-phase, three-wire source supplies a balanced load
What happens to the quantity of power supplied by a three-phase, three-wire system to a balanced load if one phase is disconnected?
A 60-Hz three-phase, three-wire system with terminals labeled 1, 2, 3 has an effective line voltage of 220 V. To determine if the system is ABC or CBA, the circuit of Fig. 11-35 is tested. Find the
A three-phase, three-wire generator with effective line voltage 6000 V is connected to a balanced load by three lines with resistances of 1 Ω each, delivering a total of 200 kW. Find the efficiency
In the two-port network shown in Fig. 12-40, R1 = 7 kΩ and R2 = 3 kΩ. Obtain the voltage ratio V2/V1(a) At no-load,(b) For RL = 20 kΩ. V₁ ww R₁ R₂ www V₂ R₁
A high-pass RL circuit has R1 = 50 kΩ and L2 = 0.2 mH.(a) Find ω if the magnitude of the voltage transfer function is |Hv∞| = 0.90.(b) With a load R = 1 MΩ across L2, find |Hv| at ω = 7.5
Find the frequency response V2/V1 for the two-port circuit shown in Fig. 12-2. V₁ 5 ΚΩ 1 μF 1250 Ω V,
In Problem 11.42, find the effective line voltage at the load.Data from Problem 11.42A balanced Δ-connected load with impedances ZΔ = 6 + j9 Ω is connected to a three-phase generator with an
A three-phase generator feeds two balanced loads (9 kW at pf = 0.8 and 12 kW at pf = 0.6, both lagging) through three cables (0.1 Ω each). The generator is regulated such that the effective line

Showing 400 - 500 of 1036