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physics
electricity and magnetism
Fundamentals Of Electric Circuits 3rd Edition Matthew Sadiku, Charles Alexander - Solutions
In the ideal autotransformer of Fig. 13.131, calculate I1, I2, and Io Find the average power delivered to the load.
In the circuit of Fig. 13.132, is adjusted until maximum average power is delivered to ZL. Find ZL and the maximum average power transferred to it. Take N1 = 600 turns and N2 = 200 turns.An asterisk indicates a challenging problem
For the circuit in Fig. 13.76, find Vo.
In the ideal transformer circuit shown in Fig. 13.133, determine the average power delivered to the load.
In the autotransformer circuit in Fig. 13.134, show that
In order to meet an emergency, three single-phase transformers with 12,470/7,200 V rms are connected in Δ -Y to form a three-phase transformer which is fed by a 12,470- V transmission line. If the transformer supplies 60 MVA to a load, find: (a) The turns ratio for each transformer, (b) The
Figure 13.135 on the following page shows a three-phase transformer that supplies a Y-connected load.(a) Identify the transformer connection.(b) Calculate currents I2 and Ic.(c) Find the average power absorbed by the load.
Consider the three-phase transformer shown in Fig. 13.136. The primary is fed by a three-phase source with line voltage of 2.4 kV rms, while the secondary supplies a three phase 120-kW balanced load at pf of 0.8. Determine:(a) The type of transformer connections,(b) The values of ILS and Ips,(c)
A balanced three-phase transformer bank with the Δ -Y connection depicted in Fig. 13.137 is used to step down line voltages from 4,500 V rms to 900 V rms. If the transformer feeds a 120-kVA load, find:(a) The turns ratio for the transformer,(b) The line currents at the primary and
A Y- Δ three-phase transformer is connected to a 60-kVA load with 0.85 power factor (leading) through a feeder whose impedance is 0.05 + j0.1 Ω per phase, as shown in Fig. 13.138. Find the magnitude of:(a) The line current at the load,(b) The line voltage at the secondary
The three-phase system of a town distributes power with a line voltage of 13.2 kV. A pole transformer connected to single wire and ground steps down the high-voltage wire to 120 V rms and serves a house as shown in Fig. 13.139.(a) Calculate the turns ratio of the pole transformer to get 120 V.(b)
Use PSpice to determine the mesh currents in the circuit of Fig. 13.140. Take ω = 1 rad/s.
Use PSpice to find I1, I2, and I3 in the circuit of Fig. 13.141.
Find v(t) for the circuit in Fig. 13.77.
Rework Prob. 13.22 using PSpiceIn problem 13.12Find current Io in the circuit of Fig. 13.91
Use PSpice to find I1, I2, and I3 in the circuit of Fig. 13.142.
Use PSpice to find V1, V2, and Io in the circuit of Fig. 13.143.
Find Ix and Vx in the circuit of Fig. 13.144 using PSpice.
Determine I1, I2, and I3 in the ideal transformer circuit of Fig. 13.145 using PSpice.
A stereo amplifier circuit with an output impedance of 7.2 k Ω is to be matched to a speaker with an input impedance of 8 Ω by a transformer whose primary side has 3,000 turns. Calculate the number of turns required on the secondary side.
A step-down power transformer with a turns ratio of n = 0.1 supplies 12.6 V rms to a resistive load. If the primary current is 2.5 A rms, how much power is delivered to the load?
A 240/120-V rms power transformer is rated at 10 kVA. Determine the turns ratio, the primary current, and the secondary current.
Find Vx in the network shown in Fig. 13.78.
A 4-kVA, 2,400/240-V rms transformer has 250 turns on the primary side. Calculate: (a) The turns ratio, (b) The number of turns on the secondary side, (c) The primary and secondary currents.
A 25,000/240-V rms distribution transformer has a primary current rating of 75 A. (a) Find the transformer kVA rating. (b) Calculate the secondary current.
A 4,800-V rms transmission line feeds a distribution transformer with 1,200 turns on the primary and 28 turns on the secondary. When a 10- Ω load is connected across the secondary, find: (a) The secondary voltage, (b) The primary and secondary currents, (c) The power supplied to the load.
A four-winding transformer (Fig. 13.146) is often used in equipment (e.g., PCs, VCRs) that may be operated from either 110 V or 220 V. This makes the equipment suitable for both domestic and foreign use. Show which connections are necessary to provide:(a) An output of 14 V with an input of 110
A 440/110-V ideal transformer can be connected to become a 550/440-V ideal autotransformer. There are four possible connections, two of which are wrong. Find the output voltage of: (a) A wrong connection, (b) The right connection. An asterisk indicates a challenging problem.
Ten bulbs in parallel are supplied by a 7,200/120-V transformer as shown in Fig. 13.147, where the bulbs are modeled by the 144- Ω resistors. Find:(a) The turns ratio n,(b) The current through the primary winding.
Find the transfer function Vo /Vi of the RC circuit in Fig. 14.68. Express it using o ω = 1/RC.Figure 14.68
Sketch the Bode magnitude and phase plots of: H(jω) = 50/ j ω(5 + jω)
Practical RC filter design should allow for source and load resistances as shown in Fig. 14.110. Let R = 4k Ω and C = 40-nF. Obtain the cutoff frequency when:(a) Rs = 0, RL = ˆž,(b) Rs = 1k Ω, R L = 5k Ω .Figure 14.110
The RC circuit in Fig. 14.111 is used for a lead compensator in a system design. Obtain the transfer function of the circuit.Figure 14.111
A low-quality-factor, double-tuned bandpass filter is shown in Fig. 14.112. Use PSpice to generate the magnitude plot of Vo (ω)Figure 14.112
Sketch the Bode plots for H(ω) = 10 + jω/jω(2 + jω)
A transfer function is given by T(s) = s + / s(s + 10) Sketch the magnitude and phase Bode plots.
Construct the Bode plots for G(s) = s + 1/s2(s + 10), s = jω
Draw the Bode plots for H(ω) = 50(jω + 1) / jω(-ω2 + 10 jω + 25)
Construct the Bode magnitude and phase plots for H(s) = 40(s + 1) / (s + 2) (s + 10), s = jω
Sketch Bode magnitude and phase plots for H(s) = 10/s(s2 + s + 16), s = jω
Sketch the Bode plots for G(s) = s/(s + 2)2 + (s + 1), s = jω
A linear network has this transfer function H(s) = 7s2 + s + 4 / (s3 + 8s2 + 14s + 5), s = jω Use MATLAB or equivalent to plot the magnitude and phase (in degrees) of the transfer function. Take 0.1 < ω < 10 rads/s.
Sketch the asymptotic Bode plots of the magnitude and phase for H(s) = 100s / (s + 10) (s + 20) (s + 40), s = jω
Sketch the magnitude Bode plot for the transfer function H(ω) = 10jω/(jω + 1)(jω + 5)2 (jω + 40)
Sketch the magnitude Bode plot for H(s) = s(s + 20) / (s + 1) (s2 + 60s) = (400), s = jω
Find the transfer function H(ω) with the Bode magnitude plot shown in Fig. 14.74.Figure 14.74
The Bode magnitude plot of H(ω ) is shown in Fig. 14.75. Find H(ω ).Figure 14.75
The magnitude plot in Fig. 14.76 represents the transfer function of a preamplifier. Find H(s).Figure 14.76
A series RLC network has R = 2 k Ω, L = 40 mH, and C = 1 μ F. Calculate the impedance at resonance and at one-fourth, one-half, twice, and four times the resonant frequency.
A coil with resistance 3Ω and inductance 100 mH is connected in series with a capacitor of 50 pF, a resistor of 6Ω and a signal generator that gives 110 V rms at all frequencies. Calculate ω0, Q, and B at resonance of the resultant series RLC circuit.
Design a series RLC resonant circuit with ω0 = 40 rad/s and B = 10 rad/s.
Design a series RLC circuit with B = 20 rad/s and ω0 = 1,000 rad/s. Find the circuit's Q. Let R = 10 Ω.
Let vs = 20 cos(at) V in the circuit of Fig. 14.77. Find ω0, Q, and B, as seen by the capacitor.Figure 14.77
For the circuit shown in Fig. 14.70, find H(s) = Vo /Vi (s).Figure 14.70
A circuit consisting of a coil with inductance 10 mH and resistance 20 Ω is connected in series with a capacitor and a generator with an rms voltage of 120 V. Find: (a) The value of the capacitance that will cause the circuit to be in resonance at 15 kHz (b) The current through the coil at
A parallel RLC circuit has the following values: R = 60 Ω, L = 1 mH, and C = 50 μF. Find the quality factor, the resonant frequency, and the bandwidth of the RLC circuit.
A parallel resonant circuit with quality factor 120 has a resonant frequency of 6 × 106 rad/s. Calculate the bandwidth and half-power frequencies.
A parallel RLC circuit is resonant at 5.6 MHz, has a Q of 80, and has a resistive branch of 40 kΩ. Determine the values of L and C in the other two branches.
A parallel RLC circuit has R = 5kΩ, L = 8 mH, and C = μF. Determine: (a) The resonant frequency (b) The bandwidth (c) The quality factor
It is expected that a parallel RLC resonant circuit has a midband admittance of 25 × 110−3 S, quality factor of 80, and a resonant frequency of 200 krad/s. Calculate the values of R, L, and C. Find the bandwidth and the half-power frequencies.
Rework Prob. 14.25 if the elements are connected in parallel. In problem A series RLC network has R = 2 k Ω, L = 40 mH, and C = 1 μ F. Calculate the impedance at resonance and at one-fourth, one-half, twice, and four times the resonant frequency.
Find the resonant frequency of the circuit in Fig. 14.78.Figure 14.78
For the "tank" circuit in Fig. 14.79, find the resonant frequency.Figure 14.79
Find the transfer function H(ω) = VO /Vi of the circuits shown in Fig. 14.71.(a)(b)
A parallel resonance circuit has a resistance of 2 k Ω and half-power frequencies of 86 kHz and 90 kHz. Determine: (a) The capacitance (b) The inductance
For the circuit shown in Fig. 14.80, next page:(a) Calculate the resonant frequency ωo, the quality factor Q, and the bandwidth B.(b) What value of capacitance must be connected in series with the 20-μF capacitor in order to double the bandwidth?Figure 14.80
For the circuits in Fig. 14.81, find the resonant frequency ωo, the quality factor Q, and the bandwidth B.Figure 14.81(a)(b)
Calculate the resonant frequency of each of the circuits in Fig. 14.82.Figure 14.82(a)(b)
* For the circuit in Fig. 14.83, find:(a) The resonant frequency ωo(b) Zin (ωo)Figure 14.83
For the circuit shown in Fig. 14.84, find ωo, B, and Q, as seen by the voltage across the inductor.Figure 14.84
For the network illustrated in Fig. 14.85, find(a) The transfer function H(ω) = Vo (ω)/I(ω),(b) The magnitude of H at ωo = 1 rad/s.Figure 14.85
Show that a series LR circuit is a lowpass filter if the output is taken across the resistor. Calculate the corner frequency fc if L = 2 mH and R = 10 k Ω.
Find the transfer function Vo /Vs of the circuit in Fig. 14.86. Show that the circuit is a lowpass filter.Figure 14.86
Determine the cutoff frequency of the lowpass filter described by H(ω) = 4/2 + jω10 Find the gain in dB and phase of H(ω) at ω = 2 rad/s.
For each of the circuits shown in Fig. 14.72, find H(s) = Vo (s)/Vs (s).(a)(b)
Determine what type of filter is in Fig. 14.87. Calculate the corner frequency fc.Figure 14.87
Design an RL lowpass filter that uses a 40-mH coil and has a cutoff frequency of 5 kHz.
Design a series RLC type bandpass filter with cutoff frequencies of 10 kHz and 11 kHz. Assuming C = 80 pF, find R, L, and Q.
Design a passive bandstop filter with ωo = 10 rad/s and Q = 20.
Determine the range of frequencies that will be passed by a series RLC bandpass filter with R = 10 Ω, L = 25mH, and C = 0.4 μ F. Find the quality factor.
(a) Show that for a bandpass filter,where B = bandwidth of the filter and ωo is the center frequency.(b) Similarly, show that for a bandstop filter,
Determine the center frequency and bandwidth of the bandpass filters in Fig. 14.88.Figure 14.88(a)(b)
The circuit parameters for a series RLC bandstop filter are R = 2 k Ω, L = 0.1 H, C = 40 pF. Calculate: (a) The center frequency (b) The half-power frequencies (c) The quality factor
Find the bandwidth and center frequency of the bandstop filter of Fig. 14.89.Figure 14.89
For the circuit shown in Fig. 14.73, find H(s) = Io (s)/Is (s).Figure 14.73
Obtain the transfer function of a highpass filter with a passband gain of 10 and a cutoff frequency of 50 rad/s.
Find the transfer function for each of the active filters in Fig. 14.90.Figure 14.90(a)(b)
The filter in Fig. 14.90(b) has a 3-dB cutoff frequency at 1 kHz. If its input is connected to a 120-mV variable frequency signal, find the output voltage at: (a) 200 Hz (b) 2 kHz (c) 10 kHz
Design an active first-order highpass filter with H(s) = -100s/ s + 10, s = jω Use a 1-μF capacitor.
Obtain the transfer function of the active filter in Fig. 14.91 on the next page. What kind of filter is it?Figure 14.91
A highpass filter is shown in Fig. 14.92. Show that the transfer function isFigure 14.92
A "general" first-order filter is shown in Fig. 14.93.(a) Show that the transfer function isS = jω(b) What condition must be satisfied for the circuit to operate as a highpass filter?(c) What condition must be satisfied for the circuit to operate as a lowpass filter?Figure 14.93
Design an active lowpass filter with dc gain of 0.25 and a corner frequency of 500 Hz.
Design an active highpass filter with a high-frequency gain of 5 and a corner frequency of 200 Hz.
Design the filter in Fig. 14.94 to meet the following requirements:(a) It must attenuate a signal at 2 kHz by 3 dB compared with its value at 10 MHz.(b) It must provide a steady-state output of v o (t) = 10 sin(2Ï€ × 108 t + 180°) V for an input vs (t) =
Calculate |H(ω)| if HdB equals (a) 0.05dB (b) -6.2 dB (c) 104.7 dB
* A second-order active filter known as a Butterworth filter is shown in Fig. 14.95.(a) Find the transfer function Vo /Vi.(b) Show that it is a lowpass filter.Figure 14.95
Use magnitude and frequency scaling on the circuit of Fig. 14.76 to obtain an equivalent circuit in which the inductor and capacitor have magnitude 1 H and 1 F respectively.
What values of Km and Kf will scale a 4-mH inductor and a 20-μ F capacitor to 1 H and 2 F respectively?
Calculate the values of R, L, and C that will result in R = 12k Ω, L = 40 μ H and C = 300 nF respectively when magnitude-scaled by 800 and frequency-scaled by 1000.
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