Questions and Answers of Schaum S Outline Of Electric Circuits

Find P delivered from a sinusoidal voltage source with Veff = 110 V to an impedance of Z = 10 + j8. Find the power factor.
A circuit with impedance Z = 8.0 − j6.0 Ω has an applied phasor voltage 70.7 ∠− 90.0° V. Obtain the complete power triangle.
Find the two elements of a series circuit having current i = 4.24 cos (5000t + 45°) A, power 180 W, and power factor 0.80 lagging.
The voltage and current across a load are given by Veff = 110 V and Ieff = 20 ∠−50° A, respectively. Find P and Q.
Obtain the power information for each element in Fig. 10-14 and construct the power triangle. 1=14.14/30° A 30 jon 3 7-120
Determine the impedance of the circuit which has a complex power S = 5031 ∠− 26.57° VA given an applied phasor voltage 212.1∠0° V.
Find the power delivered from a sinusoidal source to a resistor R. Let the effective values of the voltage and current be V and I, respectively.
Determine the impedance corresponding to apparent power 3500 VA, power factor 0.76 lagging, and effective current 18.0 A.
A series circuit of R = 10 Ω and XC = 5 Ω has an effective applied voltage of 120 V. Determine the complete power information.
A two-branch parallel circuit, with Z1 = 10 ∠0° Ω and Z2 = 8.0 ∠−30.0° Ω, has a total current i = 7.07 cos (ωt − 90°) (A). Obtain the complete power triangle.
Impedances Zi = 5.83 ∠ −59.0° Ω and Z2 = 8.94 ∠ 63.43° Ω are in series and carry an effective current of 5.0 A. Determine the complete power information.
Obtain the total power information for the parallel circuit shown in Fig. 10-16. I = 42.4/0° A US —j3 2 M Ut
A two-branch parallel circuit has branch impedances Z1 = 2.0 − j5.0 Ω and Z2 = 1.0 + j1.0 Ω. Obtain the complete power triangle for the circuit if the 2.0-Ω resistor consumes 20 W.
Find the total instantaneous power p(t), the average power P, and the reactive power Q delivered from v = (V √2) cosωt to a parallel RLC combination.
Find the power factor for the circuit shown in Fig. 10-17. 2 Ο 3 Ω j4 Ω w 10 Ω
A two-branch parallel circuit, with impedances Z1 = 4.0 ∠ −30° Ω and Z2 = 5.0 ∠ 60° Ω, has an applied effective voltage of 20 V. Obtain the power triangles for the branches and combine them
Obtain the complex power for the complete circuit of Fig. 10-25 if branch 1 takes 8.0 kvar. j5 Ω α 4 Ω jΣ Ω
If the total power in the circuit of Fig. 10-17 is 1100 W, what are the powers in the two resistors? U 01 www Ut! UE 2
A certain passive network has equivalent impedance Z = 3 + j4 Ω and an applied voltage v=42.5 cos (1000t +30°) (V)
In the circuit of Fig. 10-26, find Z if ST = 3373 Va, pf = 0.938 leading, and the 3-Ω resistor has an average power of 666 W. U 9! UE m Z
The parallel circuit in Fig. 10-27 has a total average power of 1500 W. Obtain the total power-triangle information. U 9 ܚܝܪ U£ U E! 20
Three loads are connected in parallel to a 6-kVeff ac line, as shown in Fig. 10-8. Given P₂ = 20 kW, pf₂ = 0.5 lagging; P₁ = 10kW, pf₁ = 1; Find PT. QT, ST, pf, and the current I eff P₂ =
Obtain the power factor of a two-branch parallel circuit where the first branch has Z1 = 2 + j4 Ω and the second Z2 = 6 + j0 Ω. To what value must the 6-Ω resistor be changed to result in the
Determine the average power in the 15-Ω and 8-Ω resistances in Fig. 10-28 if the total average power in the circuit is 2000 W. 15 Ω 8 Ω • -2 Ω
How much capacitive Q must be provided by the capacitor bank in Fig. 10-10 in order to improve the power factor to 0.95 lagging? 2400V 市 3.5/25° n
A three-branch parallel circuit, with Z1 = 25∠15° Ω, Z2 = 15∠60° Ω, and Z3 = 15∠90° Ω, has an applied voltage V = 339.4 ∠−30° V. Obtain the total apparent power and the overall power
A voltage, 28.28∠60° V, is applied to a two-branch parallel circuit in which Z1 = 4 ∠30°and Z2 = 5 ∠60° Ω. Obtain the power triangles for the branches and combine them into the total power
A voltage divider, useful for high-frequency applications, can be made with two capacitors C1 and C2 in the generalized two-port network of Fig. 12-12. Under open-circuit conditions, find C2 if C1 =
Find(a) The network function H(s) = V2/V1 in the circuit shown in Fig. 12-13,(b) H(jω) for LC = 2/ω02 and L/C = R2, and(c) The magnitude and phase angle of H( jω) in (b) For ω0 = 1 rad/s.
Compute the quality factor of an RLC series circuit, with R = 20 Ω, L = 50 mH, and C = 1 µF, using(a) Q = ω0L/R,(b) Q = 1/ω0CR, and(c) Q = ω0 /b. 00₁ = R 2L + R 2L + and B=0,- @= 400
Show that ω0 =√ω1ωh for the series RLC circuit.
For the series RL circuit, Fig. 12-28 (a) shows the Z-locus when ωL is fixed and R is variable; Fig. 12-28 (b) shows the Z-locus when R is fixed and L or ω is variable; and Fig. 12-28(c) shows
Find the Z-parameters of the two-port circuit in Fig. 13-2. V₁ ww 2Ω 1Η www 3 3 Ω V
Find the Z-parameters of the circuit in Fig. 13-16(a). a V₂ UI UI Ut www 352 U9 ww V₁
The Z-parameters of the two-port network N in Fig. 13-22 (a) are Z11 = 4s, Z12 = Z21 = 3s, and Z22 = 9s. Find the input current i1 for vs = cos 1000t (V) by using the open circuit impedance terminal
The two-port circuit shown in Fig. 13-3 contains a current-dependent voltage source. Find its Z-parameters. V₁ + www ΖΩ 1 H 3 Ω
The Z-parameters of a two-port network N are given by(a) Find the T-equivalent of N.(b) The network N is connected to a source and a load as shown in the circuit of Fig. 13-8. Replace N by its
Find the Z-parameters of Fig. 13-4. V₁ Ft Za Ze Zb
Express the reciprocity criteria in terms of h-, g-, and T-parameters.
Find the Z-parameters of the two-port network in Fig. 13-18. V₁ Μ 4 Ω 31₂ 1Ω ΤΩ V₂ τα
Find the Y-parameters of the circuit in Fig. 13-5. +0 οι ΖΩ لانا www 5 Ω HE F 3 Ω ΚΑΤΑ H Va
Find the T-parameters of a two-port device whose Z-parameters are Z11 = s, Z12 = Z21 = 10s, and Z22 = 100s.
Find the Z-parameters of the two-port network in Fig. 13-19 and compare the results with those of Problem 13.3.Data problem 13.3Find the Z-parameters of the two-port network in Fig. 13-18. V₁ ww 5
Find the T-parameters of a two-port device whose Z-parameters are Z11 = 106s, Z12 = Z21 = 107s, and Z22 = 108s. Compare with the results of Problem 13.21.Data from problem 13.21A load ZL is connected
The Z-parameters of a two-port device N are Z11 = ks, Z12 = Z21 = 10ks, and Z22 = 100ks. A 1-Ω resistor is connected across the output port (see Fig. 13-30).(a) Find the input impedance Zin = V1/I1
The Z-parameters of a two-port network are given by Z₁1 = 2s + 1/s Z12 = Z21 The network is connected to a source and a load as shown in Fig. 13-8. Find I₁, I₂, V₁, and V₂. = 2s 222 = 2s + 4
Find the Y-parameters of Fig. 13-19 using its Z-parameters. +Q V₁ 10 ww 552 5Ω 21₂ + + I₁₂ 2.52 1₂ V₂
The device N in Fig. 13-30 is specified by the following Z-parameters: Z22 = N2Z11 and Z12 = Z21 =√Z11Z22 =NZ11. Find Zin = VI/II when a load ZL, is connected to the output terminal. Show that if
Find the Y-parameters of the two-port network in Fig. 13-20 and thus show that the networks of Figs. 13-19 and 13-20 are equivalent.Data from figure 13-19Data from figure 13-20
Find the h-parameters of Fig. 13-9. 1 Τ U OS 3001, V2
Find the Z-parameters in the circuit of Fig. 13-31. +81= V₁ 10 4 Ω -5 202 www www 202 ΖΩ Irm 402 4Ω HE + +815 V₂
Apply the short-circuit equations (10) to find the Y-parameters of the two-port network in Fig. 13-21. V₁ 1 12 Ω www 12 Ω 3 Ω V₂
Apply KCL at the nodes of the network in Fig. 13-21 to obtain its terminal characteristics and Y-parameters. Show that the two-port networks of Figs. 13-18 to 13-21 are all equivalent.Data from
Find the g-parameters in the circuit shown in Fig. 13-10. V₁ ΤΟ 109 Ω 10-3V, 10 Ω I Va 10
Find the Y-parameters in the circuit of Fig. 13-32. 1001 F - نما D не ΤΩ ww www F не - الي 2 не المية F ΤΩ www ΤΩ www HE 001 T
Find the T-parameters of Fig. 13-11 where Za and Zb are nonzero. V₁ Za Zb V₂ 10
Two two-port networks a and b with transmission parameters Ta and Tb are connected in cascade (see Fig. 13-14). Given I2a = −I1b and V2a = V1b, find the T-parameters of the resulting two-port
Find the Z- and Y-parameters of Fig. 13-15. | Ο σε 3 Ω www 3 Ω ΖΩ TIL V2 10
Find the T-and Z-parameters of the network in Fig. 13-33. The impedances of the capacitors are given. KU!- www UI in www UI 카 jn UI 10 ㅠㅠ
Two two-port networks a and b, with short-circuit admittances Ya and Yb, respectively, are connected in parallel (see Fig. 13-13). Derive the Y-parameter equations (32a).Data from figure 13-13
Find the Z-parameters of the two-port circuit of Fig. 13-34. 20 Za Za farby 10 V₂
Find(a) The Z-parameters of the circuit of Fig. 13-23 (a) and(b) An equivalent model which uses three positive-valued resistors and one dependent voltage source. W 252 21₂ (a) 20 W UE V₂ 10
Find the Z-parameters of the two-port circuit of Fig. 13-35. V₁ 10 2₂ Za Za Z₂ 10
(a) Obtain the Y-parameters of the circuit in Fig. 13-23 (a) from its Z-parameters.(b) Find an equivalent model which uses two positive-valued resistors and one dependent current source.
Referring to the two-port circuit of Fig. 13-36, find the T-parameters as a function of ω and specify their values at ω = 1, 103, and 106 rad/s. IL 10-30 www 10-3 H 106F 카 2
Referring to the network of Fig. 13-23(b), convert the voltage source and its series resistor to its Norton equivalent and show that the resulting network is identical to that in Fig. 13-24.Data from
A two-port network contains resistors, capacitors, and inductors only. With port #2 open [Fig. 13-37(a)], a unit step voltage v1 = u(t) produces i1 = e−tu(t) (μA) and v2 = (1 − e−t) u(t) (V).
The h-parameters of a two-port network are given. Show that the network may be modeled by the network in Fig. 13-26 where h11 is an impedance, h12 is a voltage gain, h21 is a current gain, and h22 is
The two-port network N in Fig. 13-38 is specified by Z11 = 2, Z12 = Z21 = 1, and Z22 = 4. Find I1, I2, and I3. V = 141 v( + 3 Ω I 3 Ω ww N V₂ 6Ω
Find the h-parameters of the circuit in Fig. 13-25. V₁ 1 402 Ω IN = 0,1V, 5Ω 2
Find the h-parameters of the circuit in Fig. 13-25 from its Z-parameters and compare with the results of Problem 13.16.Data from problem 13.16Find the h-parameters of the circuit in Fig. 13-25.
The simplified model of a bipolar junction transistor for small signals is shown in Fig. 13-27.Find its h-parameters. I₁ V₁ 1 1 BI₁
The device H of Problem 13-19 is placed in the circuit of Fig. 13-29(a). Replace H by its model of Fig. 13-28 and find V2/Vs.Data from problem 13.19The h-parameters of a two-port device H are given
The h-parameters of a two-port device H are given byDraw a circuit model of the device made of two resistors and two dependent sources. Include the values of each element h = 500 Ω hy = 104 hy =
A load ZL is connected to the output of a two-port device N (Fig. 13-30) whose terminal characteristics are given by V1 = (1/N)V2 and I1 = −NI2. Find(a) The T-parameters of N and(b) The input
When one coil of a magnetically coupled pair has a current 5.0 A the resulting fluxes Φ11 and Φ12 are 0.2 mWb and 0.4 mWb, respectively. If the turns are N1 = 500 and N2 = 1500, find L1, L2, M, and
Given L1 = 0.1 H, L2 = 0.5 H, and i1(t) = i2(t) = sin ω t in the coupled coils of Fig. 14-2. Find v1(t) and v2(t) for(a) M = 0.01 H,(b) M = 0.2 H, and(c) M = -0.2 H.Data from figure 14.2
Two coupled coils, L1 = 0.8 H and L2 = 0.2 H, have a coefficient of coupling k = 0.90. Find the mutual inductance M and the turns ratio N1/N2.
Two coupled coils have self-inductances L1 = 50 mH and L2 = 200 mH, and a coefficient of coupling k = 0.50. If coil 2 has 1000 turns, and i1 = 5.0 sin 400t (A), find the voltage at coil 2 and the
Suppose the switch in the passive loop to be closed at an instant (t = 0) when i1 = 0. For t > 0, the sequence of the passive loop is (see Fig. 14-6) M di L₂ R₂ ww iz Fig. 14-6
Two coupled coils, N1 = 100 and N2 = 800, have a coupling coefficient k = 0.85. With coil 1 open and a current of 5.0 A in coil 2, the flux is Φ2 = 0.35 mWb. Find L1, L2, and M.
The current directions chosen in Fig. 14-8 (a) are such that the signs on the M-terms are opposite to the signs on the L-terms and the dots indicate the terminals with the same instantaneous
Two identical coupled coils have an equivalent inductance of 80 mH when connected series aiding, and 35 mH in series opposing. Find L1, L2, M, and k.
Apply KVL to the series circuit of Fig. 14-18. +1 R M L₁ L₂
In a pair of coils, with L1 = 0.1 H and L2 = 0.2 H, at a certain moment, i1 = 4 A and i2 = 10 A. Find the total energy in the coils if the coupling coefficient M is(a) 0.1 H,(b) √2 /10
Two coupled coils, with L1 = 20 mH, L2 = 10 mH, and k = 0.50, are connected four different ways: series aiding, series opposing, and parallel with both arrangements of winding sense. Obtain the
Draw the voltage-current phasor diagram corresponding to Fig. 14-11(a), and from it derive the input impedance of the transformer. + V₁ R₁ I₁ jX₁| E₁ +1 a +1 jX22 E₂ 1₂ R₂ w ZL + N
In a series aiding connection, two coupled coils have an equivalent inductance LA; in a series opposing connection, LB. Obtain an expression for M in terms of LA and LB.
Write the mesh current equations for the coupled circuit shown in Fig. 14-37. Obtain the dotted equivalent circuit and write the same equations. R₁ L₁ C M 1+ Ry L2 2 R₂
(a) Write the mesh current equations for the coupled coils with currents i1 and i2 shown in Fig. 14-19.(b) Repeat for i2 as indicated by the dashed arrow. 20 + iz www R₁ L₁ M L₂ R:
The ideal transformer may be considered as the limiting case of the linear transformer of Section 14.7. Thus, in (14a) setthat is, the ampere turns of the primary equal the ampere turns of the
Write the phasor equation for the single-loop, coupled circuit shown in Fig. 14-38. j5 . | 1 k = 0.65 10 0 50/0 V j3 K -j8 .
Obtain the dotted equivalent circuit for the coupled circuit shown in Fig. 14-20, and use it to find the voltage V across the 10-Ω capacitive reactance. 10/0° _V + US US! j2 0 -j10 Q 5 Ꮭ j5 Ꮔ +
Obtain the dotted equivalent circuit for the coupled circuit of Fig. 14-38. j5 2 . k = (0.65 ww 10 2 +- 50/0° V j3 2 —j8 2
The three-winding transformer shown in Fig. 14-14 has turns N1 = 20, N2 = N3 = 10. Find I1 given that I2 = 10.0∠-53.13° A, = 10.0 ∠-45° A. N₁ N₂ 1₂ N₂ 13 Fig. 14-14
Obtain the dotted equivalent for the circuit shown in Fig. 14-22 and use the equivalent to find the equivalent inductive reactance. j3 Ω j2 Ω -j4 - j3 Ω j5 Ω Fig. 14-22 j6 Ω
(a) Compute the voltage V for the coupled circuit shown in Fig. 14-24.(b) Repeat with the polarity of one coil reversed. 50/0°_v (+ j5 Ω k = 0.8 Fig. 14-24 3 Ω j10 Ω -j4 Ω 12 5 Ω3V
Given L1 = 0.2 H, L2 = 0.1 H, M = 0.1 H, and R = 10 Ω in the circuit of Fig. 14-17. Find i1 for v1 = 142.3 sin 100t. U₁ M L₂ Fig. 14-17 R
The three coupled coils shown in Fig. 14-40 have coupling coefficients of 0.50. Obtain the equivalent inductance between the terminals AB. 200 mH 50 mH 100 mH B
Obtain two forms of the dotted equivalent circuit for the coupled coils shown in Fig. 14-40. A 200 mH 50 mH 100 mH B

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