- Use .TRAN and .PROBE to plot VC across the 1-μF capacitor in the source-free circuit of Fig. 15-30(a) for R = 100, 600, 1100, 1600, and 2100 Ω. The initial voltage is VC(0) = 10 V.Figure 15-30 + Vc
- Z-parameters of the two-port network N in Fig. 13-22 (a) are Z11 = 4s, Z12 = Z21 = 3s, and Z22 = 9s.(a) Replace N by its T-equivalent.(b) Use part (a) to find input current i1 for vs = cos 1000t
- Referring to Example 13.4, find the Z-parameters of the circuit of Fig. 13-5 from its Y-parameters.Data from Example 13.4Find the Y-parameters of the circuit in Fig. 13-5. 202 H 50 Fig. 13-5 HE -16
- (a) A sinusoidal voltage with Veff = 10 V is connected across Z1 = 1 + j as shown in Fig. 10-7(a). Find i1, I1,eff, p1(t), P1, Q1, power factor pf1, and S1.(b) Repeat part (a) replacing the load Z1
- Draw an approximate plot of v(t) = e−t/τ for t > 0Identify the initial point A (t = 0, v = 1) of the curve and the intersection B of its tangent with the t axis at t = τ. Draw the tangent line
- Consider a linear circuit with the following input-output pair valid for all ω and A: Input: v(t) = A cos cot Output: vo(t) = A cos (@ot - 0)
- Convert the amplifier circuit of Fig. 5-11 into a noninverting configuration and assume the same conditions as specified in Example 5.27 with v1(t) as the input, v2(t) as the output, Ri = ∞, Ro =
- In the inverting amplifier circuit of Fig. 5-11, v1(t) is the input and v2(t) is the output. Let Ri = ∞, Ro = 0, and assume the 741 op amp model specified by Example 5.26.(a) Find the circuit’s
- Plot the closed-loop frequency response V3/Vac in Fig. 15-34 (a) for f as it varies from 1 MHz to 1 GHz, using the subcircuit model shown in Fig. 15-34(b). Compare with the open-loop frequency
- Write the source file for the circuit in Fig. 15-9 (a) using commands .DC, .PLOT, and .PROBE to find the I-V characteristic equation for I varying from 0 to -2 A at the terminal AB.
- Obtain Hv∞ for a high-pass RL circuit at ω = 2.5ωx, R = 2 kΩ, L = 0.05 H.
- A balanced Y-connected load, with impedances 6.0∠45° Ω, is connected to a three-phase, four-wire CBA system having effective line voltage 208 V. Obtain the four line currents.
- A three-phase, three-wire system, with an effective line voltage 100 V, has currentsWhat is the sequence of the system and what are the impedances, if the connection is delta?
- Three impedances of 4.20 ∠ −35° Ω are connected in delta to a three-phase, ABC system having VBC = 495.0 ∠ 0° V. Obtain the line currents.
- Three impedances of 10.0 ∠ 53.13° Ω are connected in delta to a three-phase, CBA system with an affective line voltage 240 V. Obtain the line currents.
- Rework Example 11.3 by the single-line equivalent method.Data from Example 11.3A three-phase, four-wire, CBA system, with an effective line voltage of 120 V, has three impedances of 20 ∠−30° Ω
- A three-phase, four-wire, CBA system, with an effective line voltage of 120 V, has three impedances of 20 ∠−30° Ω in a Y -connection (Fig. 11-10). Determine the line currents and draw the
- A three-phase, three-wire, ABC system, with an effective line voltage of 120 V, has three impedances of 5.0∠45° Ω in a Δ-connection. Determine the line currents and draw the voltage-current
- An ac generator contains two voltage sources with voltages of the same amplitude and frequency, but 90° out of phase. The references of the sources are connected together to form the generator’s
- Find the maximum energy (E) stored in the inductor of Example 10.17 (a) and show that it is greater than the sum of the maximum stored energies (E1 and E2) when each source is applied alone.Data
- A 100-kVA transformer is at 80 percent of rated load at a power factor 0.85 lagging. How many kVA in additional load at 0.60 lagging power factor will bring the transformer to the full rated load?
- In Problem 10.39, what percent reduction in the line current and total voltamperes is achieved in part (a)? What further reduction is achieved in part (b)?Data from problem 10.39A 4500-VA load at
- A 4500-VA load at power factor 0.75 lagging is supplied by a 60-Hz source with effective voltage 240 V. Determine the parallel capacitance in microfarads necessary to improve the power factor
- Obtain the complete power triangle for the following parallel-connected loads: load #1, 200 VA, pf = 0.70 lagging; load #2, 350 VA, pf = 0.50 lagging; load #3, 275 VA, pf = 1.00.
- Obtain the complete power triangle for the following parallel-connected loads: load #1, 200 VA, pf = 0.70 lagging; load #2, 350 VA, pf = 0.50 lagging; load #3, 275 VA, pf = 1.00.
- Obtain the complete power triangle for the following parallel-connected loads: load #1, 200 VA, pf = 0.70 lagging; load #2, 350 VA, pf = 0.50 lagging; load #3, 275 VA, pf = 1.00.
- A circuit with impedance Z = 10.0 ∠60° Ω has its power factor improved by a parallel capacitive reactance of 20°Ω. What is the resulting reduction in the current?
- A load of 300 kW, with an initial power factor 0.65 lagging, has its power factor improved to 0.90 lagging by parallel capacitors. How many kvar must these capacitors furnish and what is the
- Obtain the complete power triangle for the circuit shown in Fig. 10-20, if the total reactive power is 2500 var (inductive). Find the branch powers P1 and P2.
- A fourth load Q4 is added in parallel to the three parallel loads of Example 10.12 such that the total power factor becomes 0.8 lagging while the total power remains the same. Find Q4 and the
- Find the ac power delivered in a capacitor C.
- Find the ac power entering an inductor L.
- Obtain the complete power triangle for the following parallel-connected loads: load #1, 5 kW, pf = 0.80 lagging; load #2, 4 kVA, 2 kvar (capacitive); load #3, 6 kVA, pf = 0.90 lagging.
- Determine the total power information for three parallel-connected loads: load #1, 250 VA, pf = 0.50 lagging; load #2, 180 W, pf = 0.80 leading; load #3, 300 VA, 100 var (inductive). Calculate the
- A load with P = 1000 kW and pf = 0.5 lagging is fed by a 5-kV source. A capacitor is added in parallel such that the power factor is improved to 0.8. Find the reduction in current drawn from the
- Obtain a conductively coupled equivalent circuit for the magnetically coupled circuit shown in Fig. 14-31. 50/0° _V +1 Us! j6 Ω Τ Fig. 14-31 3 Ω j10 Ω m -j4 Ω Ε US
- A balanced Y-connected load, with impedances 65.0∠−20° Ω, is connected to a three-phase, three-wire, CBA system, where VAB = 678.8 ∠ −120° V. Obtain the three line currents.
- Show that the line-to-line voltage VL in a three-phase system is 3 times the line-to-neutral voltage VPh.
- Repeat Problem 11.2 but this time with the two voltage sources of Problem 11.1 90° out of phase.Data from Problem 11.1The two-phase balanced ac generator of Fig. 11-22 feeds two identical loads. The
- Solve Problem 11.1 given Vp = 110 Vrms and Z = 4 + j3 Ω.Data from Problem 11.1The two-phase balanced ac generator of Fig. 11-22 feeds two identical loads. The two voltage sources are 180° out of
- The two-phase balanced ac generator of Fig. 11-22 feeds two identical loads. The two voltage sources are 180° out of phase. Find(a) The line currents, voltages, and their phase angles, and(b) The
- A practical voltage source is modeled by an ideal voltage source Vg with an open-circuited effective value of 320 V in series with an output impedance Zg = 50 + 100 Ω. The source feeds a load Zl =
- A single-phase ac source having effective value 6 kV delivers 100 kW at a power factor 0.8 lagging to two parallel loads. The individual power factors of the loads are pf1 = 0.7 lagging and pf2 = 0.1
- In the circuit of Fig.10-29, va = 10√2 cos t and ib = 10 √2 cos 2t.(a) Find the average power delivered by each source.(b) Find the current in the resistor and the average power absorbed by
- In the circuit of Fig. 10-29 the voltage source has effective value 10 V at ω = 1 rad/s and the current source is zero.(a) Find the average and reactive powers delivered by the voltage
- The terminal voltage and current of a two-terminal circuit are Vrms = 120 V and Irms = 30∠ −60° A at f = 60 Hz, respectively. Compute the complex power. Find the impedance of the circuit and its
- An induction motor load of 2000 kVA has power factor 0.80 lagging. Synchronous motors totaling 500 kVA are added and operated at a leading power factor. If the overall power factor is then 0.90
- A 65-kVA load with a lagging power factor is combined with a 25-kVA synchronous motor load which operates at pf = 0.60 leading. Find the power factor of the 65-kVA load, if the overall power factor
- A 250-kVA transformer is at full load with power factor 0.80 lagging.(a) How many kvar of capacitors must be added to improve this power factor to 0.90 lagging? (b) After improvement of the power
- An induction motor with a shaft power output of 1.56 kW has an efficiency of 85 percent. At this load, the power factor is 0.80 lagging. Give the complete input power information.
- A 500-kVA transformer is at full load and a 0.60 lagging power factor. A capacitor bank is added, improving the power factor to 0.90 lagging. After improvement, what percent of rated kVA is the
- Referring to Problem 10.20, if the additional load has a power factor 0.866 leading, how many kVA may be added without exceeding the transformer rating?Data from Problem 10.20A transformer rated at a
- A 25-kVA load with power factor 0.80 lagging has a group of resistive heating units added at unity power factor. How many kW do these units take, if the new overall power factor is 0.85 lagging?
- A transformer rated at a maximum of 25 kVA supplies a 12-kW load at power factor 0.60 lagging. What percent of the transformer rating does this load represent? How many kW in additional load may be
- The addition of a 20-kvar capacitor bank improves the power factor of a certain load to 0.90 lagging. Determine the complex power before the addition of the capacitors, if the final apparent power is
- Find the capacitance C necessary to improve the power factor to 0.95 lagging in the circuit shown in Fig. 10-22, if the effective voltage of 120 V has a frequency of 60 Hz. Veft = 120 V -jxc 20/30⁰
- A practical coil is placed between two voltage sources v1 = 5 cos ω1 t and v2 = 10 cos (ω2t = 60°) which share the same common reference terminal (see Fig. 9-54). The coil is modeled by a 5-mH
- A generator, with Vg = 100 V(rms) and Zg = 1 + j, feeds a load Z1 = 2 (Fig. 10-12).(a) Find the average power PZ1 (absorbed by Z1), the power Pg (dissipated in Zg) and PT (the power provided by the
- Obtain the complete power triangle and the total current for the parallel circuit shown in Fig. 10-19, if for branch 2, S2 = 1490 VA. 1y ΖΩ j3 Ω 2 3 Ω j6 Ω
- A three-phase, 339.4-V, ABC system [Fig. 11-15(a)] has a Δ-connected load, withObtain the phase and line currents and draw the phasor diagram. ZAB = 10/0° 2 ZBC = 10/30° 2 Ω ZCA 15-30° 2
- A three-phase, ABC system, with an effective voltage 70.7 V, has a balanced Δ-connected load with impedances 20∠45° Ω. Obtain the line currents and draw the voltage-current phasor diagram.
- A three-phase, three-wire CBA system, with an effective line voltage 106.1 V, has a balanced Y-connected load with impedances 5 ∠−30° Ω (Fig. 11-26). Obtain the currents and draw the voltage
- A balanced Δ-connected load, with ZΔ = 9.0 ∠ −30° , and a balanced Y-connected load, with ZY = 5.0 ∠ 45° Ω, are supplied by the same three-phase, ABC system, with effective line voltage
- A three-phase, four-wire, 150-V, CBA system has a Y-connected load, with Z = 6/0° Ω Zg = 6 /30° Ω Z = 5/45° Ω
- Figure 11-17 (a) shows the same system as in Example 11.6 except that the neutral wire is no longer present. Obtain the line currents and find the displacement neutral voltage, VON.Data from Example
- A balanced Δ-connected load having impedances 27.0 ∠ −25° Ω, and a balanced Y-connected load having impedances 10.0 ∠ −30° Ω are supplied by the same three-phase, ABC system, with VCN
- A three-phase, three-wire CBA system, with an effective line voltage 106.1 V, has a balanced Δ-connected load with impedances Z = 15∠30° Ω. Obtain the line and phase currents by the singleline
- A three-phase, three-wire system, with an effective line voltage 176.8 V, supplies two balanced loads, one in delta configuration with ZΔ = 15 ∠ 0° Ω and the other in wye form with ZY = 10 ∠
- A three-phase, ABC system, with effective line voltage 500 V, has a Δ-connected load for whichObtain the line currents. LAB = 10.0 /30° Ω ZBC=25.0/0° 2 ZCA = 20.0/-30°
- A balanced Δ-connected load, with impedances 10.0 ∠−36.9° Ω, and a balanced Y-connected load are supplied by the same three-phase, ABC system having VCA = 141.4 ∠ 240° V. If IB = 40.44 ∠
- A three-phase, ABC system, with VBC = 294.2∠0° V, has the Δ-connected loadObtain the line currents. AB=5.0/0° $2 BC=4.0/30° 2 ZCA = 6.0/-15°
- Obtain the readings when the two-wattmeter method is applied to the circuit of Problem 11.8.Data from Problem 11.8A three-phase, three-wire system, with an effective line voltage 176.8 V, supplies
- A three-phase supply, with an effective line voltage 240 V, has an unbalanced Δ-connected load shown in Fig. 11-30. Obtain the line currents and the total power. VCA B VAB VBC ICA LAB J IBC 25/90°
- A three-phase, four-wire, CBA system, with effective line voltage 100 V, has Y-connected impedancesObtain the currents IA, IB, IC, and IN . Z = 3.0/0° Ω Zg = 3.61/56.31° Ω Z=2.24/-26.57° Ω
- Obtain the readings of wattmeters placed in lines A and B of the circuit of Problem 11.10. (Line C is the potential reference for both meters.)Data from Problem 11.10A three-phase supply, with an
- A three-phase, four-wire, ABC system, with VBC = 294.2∠0° V, has Y-connected impedancesObtain the currents IA, IB, IC, and IN . Z = 12.0/45° Ω Zg = 10.0/30° Ω Zc=8.0/0° Ω
- A three-phase, four-wire, ABC system, with line voltage VBC = 294.2 ∠ 0° V, has a Y-connected load of ZA = 10∠0° Ω, ZB = 15∠30° Ω, and ZC = 10∠−30° Ω (Fig. 11-31). Obtain the line
- A Y-connected load, with ZA = 10 ∠ 0° Ω, ZB = 10 ∠ 60°, and ZC = 10 ∠ −60° Ω, is connected to a three-phase, three-wire, ABC system having effective line voltage 141.4 V. Find the load
- The Y-connected load impedances ZA = 10 ∠ 0° Ω, ZB = 15∠30° Ω, and ZC = 10 ∠ −30° Ω, in Fig. 11-32, are supplied by a three-phase, three-wire, ABC system in which VBC = 208 ∠ 0° V.
- Obtain the total average power for the unbalanced, Y-connected load in Problem 11.13, and compare with the readings of wattmeters in lines B and C.Data from problem 11.13The Y-connected load
- A Y-connected load, with ZA = 10 ∠ −60° Ω, ZB = 10 ∠ 0° Ω, and ZC = 10 ∠ 60° Ω, is connected to a threephase, three-wire, CBA system having effective line voltage 147.1 V. Obtain the
- A three-phase, three-wire, ABC system with a balanced load has effective line voltage 200 V and (maximum) line current IA = 13.61 ∠ 60° A. Obtain the total power.
- Two two-port networks a and b, with open-circuit impedances Za and Zb, respectively, are connected in series (see Fig. 13-12). Derive the Z-parameter equations (31a).Data from figure 13-12
- A three-phase, three-wire, balanced, Δ-connected load yields wattmeter readings of 1154 W and 557 W. Obtain the load impedance, if the line voltage is 141.4 V.
- An RC transient identical to that in Problems 7.1 and 7.2 has a power transientData from Problem 7.1At t = 0−, just before the switch is closed in Fig. 7-20, vC = 100 V. Obtain the current and
- Find a function v(t) which decays exponentially from 5 V at t = 0 to 1 V at t = ∞ with a time constant of 3 s. Plot v(t) using the technique of Example 6.20.Data from Example 6.20Draw an
- By observing that the circuit of 7-51 (a) is an inverting Schmitt trigger (introduced in Problem 5.58), argue that the capacitor voltage and the op amp’s output are correctly shown in Fig.
- A 90 μF capacitor having 6+ volts across its terminals is connected at t = 0 to the input of the circuit of Fig. 5-57, reproduced below in Fig. 7-50(a). Assume R1 = R2 = R3 = 1 kΩ and an ideal op
- In the RLC circuit of Fig. 8-30, the capacitor is initially charged to V0 = 200 V. Find the current transient after the switch is closed at t = 0. Vo + 200 Ω 0.1 H 5 με
- In the circuit of Fig. 9-55, v1 = V1 cos (2t) and v2 = V2 cos (0.25t). Find vA. 2₁ 1 + 6 H roo 000 0.5 F 1 F 4 H +1 V2
- Figure 10-2 (a) shows the graph of a current in a 1 kΩ resistor. Find and plot the instantaneous power p(t). +1 i, mA 2 (a) 3 + 5 t, ms.
- The current plotted in Fig. 10-2 (a) enters a 0.5-μF capacitor in series with a 1-kΩ resistor. Find and plot(a) v across the series RC combination and(b) The instantaneous power p entering the
- The current in Example 10.1 passes through a 0.5-μF capacitor. Find the power p(t) entering the capacitor and the energy w(t) stored in it. Assume vC(0) = 0. Plot p(t) and w(t).Data from Example
- Given a circuit with an applied voltage v = 14.14 cos ω t (V) and a resulting current i = 17.1 cos (ωt − 14.05°) (mA), determine the complete power triangle.
- Given a circuit with an applied voltage v = 340 sin (ωt − 60°) (V) and a resulting current i =13.3 sin (ωt − 48.7°) (A), determine the complete power triangle.
- A 1-V ac voltage source feeds(a) A 1-Ω resistor,(b) S load Z = 1 + j, and(c) A load Z = 1 − j. Find P in each of the three cases.
- A voltage v = 140 cos ω t is connected across an impedance Z = 5∠−60° . Find p(t).
- A two-element series circuit with R = 5.0 Ω and XL = 15.0 Ω, has an effective voltage 31.6 V across the resistance. Find the complex power and the power factor.
- Obtain the complete power information for a passive circuit with an applied voltage v = 150 cos (ωt + 10°) V and a resulting current i = 5.0 cos (ωt − 50°) A.
- A two-element series circuit has average power 940 W and power factor 0.707 leading. Determine the circuit elements if the applied voltage is v = 99.0 cos (6000t + 30°) V.

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