Questions and Answers of Schaum S Outline Of Electric Circuits

A balanced Δ-connected load has impedances 45 + j60 Ω. Find the average power delivered to it at an effective line voltage of:(a) 400 V,(b) 390 V.
Obtain the change in average power delivered to a three-phase balanced load if the line voltage is multiplied by a factor α.
A low-pass RC circuit under no-load conditions has R1 = 5 kΩ.(a) Find C2 if |Hv| = 0.5 at 10 kHz.(b) Obtain Hv at 5 kHz.(c) What value of C2 results in |Hv| = 0.90 at 8 kHz?(d) With C2 as in
Two circuit elements in a series connection have current and total voltageIdentify the two elements. i = 4.0 cos (2000t + 13.2°) (A) v = 200 sin (2000t + 50.0°) (V)
If the current driving a series RC circuit is given by i = I sinω t, obtain the total voltage across the two elements.
Find the two elements in a series circuit, given that the current and total voltage are i = 10 cos (5000t - 23.13°) (A) v = 50 cos (5000t +30°) (V)
A series combination of R = 10Ω and L = 20 mH has a current i = 5.0 cos (500t + 10°) (A). Obtain the voltages v and V, the phasor current I and sketch the phasor diagram.
A series RC circuit, with R = 27.5 Ω and C = 66.7 mF, has sinusoidal voltages and current, with angular frequency 1500 rad/s. Find the phase angle by which the current leads the voltage.
A series circuit, with R = 2.0 Ω and C = 200 pF, has a sinusoidal applied voltage with a frequency of 99.47 MHz. If the maximum voltage across the capacitance is 24 V, what is the maximum voltage
A series RLC circuit, with R = 15 Ω, L = 80 mH, and C = 30 mF, has a sinusoidal current at angular frequency 500 rad/s. Determine the phase angle and whether the current leads or lags the total
Given V1 = 25.0 ∠143.13° and V2 = 11.2 ∠26.57°, find the ratio V1/V2 and the sum V1 + V2.
A capacitance C = 35 mF is in parallel with a certain element. Identify the element, given that the voltage across and total current through the combination are v= 150 sin 3000t (V) i = 16.5 sin
The current in a series circuit of R = 5 Ω and L = 30 mH lags the applied voltage by 80°. Determine the source frequency and the impedance Z.
The phasor voltage across the terminals of a network such as that shown in Fig. 9-7 (b) is 100.0 ∠45° V and the resulting current is 5.0∠15° A. Find the equivalent impedance and admittance.
The total current I entering the circuit shown in Fig. 9-20 is 33.0 ∠−13.0 A. Obtain the branch current I3 and the voltage V. OI j5 Ո 2 5 Զ j8.66 2 3 15 Ո —j10 2
At what frequency will the current lead the voltage by 30° in a series circuit with R = 8 Ω and C = 30 mF?
A two-element series circuit, with R = 20 Ω and L = 20 mH, has an impedance 40.0 ∠θ Ω°. Determine the angle θ and the frequency.
Find Z1 in the three-branch network of Fig. 9-21, if I = 31.5 ∠24.0° A for an applied voltage V = 50.0 ∠60.0° V. + V 1 Ζ 10 Ω 4.0 Ω 13.0 Ω
Obtain the conductance and susceptance corresponding to a voltage V = 85.0 ∠ 205° V and a resulting current I = 41.2 ∠−141.0° A.
A practical coil contains resistance as well as inductance and can be represented by either a series or parallel circuit, as suggested in Fig. 9-42. Obtain Rp and Lp in terms of Rs and Ls.
The constants R and L of a coil can be obtained by connecting the coil in series with a known resistance and measuring the coil voltage Vx, the resistor voltage V1, and the total voltage VT (Fig.
In the network shown in Fig. 9-43, the 60-Hz current magnitudes are known to be IT = 29.9 A, I1 = 22.3 A, and I2 = 8.0 A. Obtain the circuit constants R and L. IT R jol 1₂ 15 f
In the parallel circuit shown in Fig. 9-24, the effective values of the currents are Ix = 18.0 A, I1 = 15.0 A, and IT = 30.0 A. Determine R and XL. IT jXL 4.0 Ω U
Obtain the magnitude of the voltage VAB in the two-branch parallel network of Fig. 9-44, if XL is(a) 5 Ω,(b) 15 Ω,(c) 0 Ω. 100/0° v(+ 50 Ω A 50 Ω 15 Ω B jXL
Obtain the phasor voltage VAB in the two-branch parallel circuit of Fig. 9-26. 18/45° A 10 Ω A 20 Ω Y X Į 2 Ω B j6 Ω
In the network shown in Fig. 9-45, VAB = 36.1∠ 3.18° V. Find the source voltage V. + 10 Ω A 5Ω j4 Ω Β 3 Ω
In the parallel circuit shown in Fig. 9-27, VAB = 48.3 ∠30°V. Find the applied voltage V. V 2 4 Ո —j4 2 X 5 B j8.66 2
For the network of Fig. 9-46 assign two different sets of mesh currents and show that for each, Δz = 55.9 ∠-26.57° Ω2. For each choice, calculate the phasor voltage V. Obtain the phasor voltage
Obtain the voltage Vx in the network of Fig. 9-28 using the mesh current method. 10/0° _v( + V ΣΩ N -j2 Ω I₁ 5 Ω 13 5/30° V j5 Ω 12 την Ε ΣΩ 10 Ω www + V – -12 Ω www 10 Ω
For the network of Fig. 9-47, use the mesh current method to find the current in the 2 + j3 Ω impedance due to each of the sources V1 and V2. V = 30/0° V 5 2 2 2 j3 a 000 j5 2 1: I, 4 ) 6 2 13 + )
In the network of Fig. 9-29, determine the voltage V which results in a zero current through the 2 + j3 Ω impedance. 30/0° VI + US 2+j3 Ω j5 Ω I U9 4 Ω I
Solve Problem 9.19 by the node voltage method.Data from Problem 9.19In the network of Fig. 9-29, determine the voltage V which results in a zero current through the 2 + j3 Ω impedance. 30/0° VI
For the network of Fig. 9-49, obtain the current ratio I1/I3. jΞ Ω -j4 Ω HE 5Ω I ΦΩ jΖ Ω Ι
Use the node voltage method to obtain the current I in the network of Fig. 9-31. 50/0° V 5 Ω 4 Ω Ω w j2 Ω 2 ref. 2 2 Ω -w -j2 Ω +1 50/90° V
In the network shown in Fig. 9-48, the two equal capacitances C and the shunting resistance R are adjusted until the detector current ID is zero. Assuming a source angular frequency ω, determine the
Find the input impedance at terminals ab for the network of Fig. 9-32. a b UZ!- Us itt 1₁ 3 Ω j5 Ω ref. 50 1₂ US 202 -12 02 Vo
For the network of Fig. 9-49, obtain Zinput,1 and Ztransfer,13. Show that Ztransfer,31 = Ztransfer,13. jΞ Ω -j4 Ω HE 5Ω 1 ΣΩ jΖ Ω Ι
For the network in Fig. 9-32, obtain the current in the inductor, Ix, by first obtaining the transfer impedance. Let V = 10 ∠30° V. . b 5 2 −j2 2 j5 Ո 3 2 1, ref. 5 Ո I 2 2 -j2 2 Vo
In the network of Fig. 9-50, obtain the voltage ratio V1/V2 by application of the node voltage method. 5 Ω 1 4Ω j2 Ω ref. 2 15 Ω 10 Ω
For the network in Fig. 9-32, find the value of the source voltage V which results in V0 = 5.0 ∠0° V. . 5 2 −j2 2 b " j5 2 £ 3 2 1, ref. I US 2 2 —j2 2
For the network of Fig. 9-50, obtain the driving-point impedance Zinput,1. 5 Ω 1 4Ω j2 Ω ref. 2 j5 Ω 10 Ω
For the network shown in Fig. 9-33, obtain the input admittance and use it to compute node voltage V1. 5/0° A 10 Ω 2 Ω ww | j5 Ω ref. j4 Ω 3 Ω - -j10 Ω
Obtain the Thévenin and Norton equivalent circuits at terminals ab for the network of Fig. 9-51. Choose the polarity such that V′ = Vab. 55.8/-17.4° 55.8) −17.4° V (+ 1+ 5 Զ 2 Ո j5 2 j3
For the network of Problem 9.25, compute the transfer admittance Ytransfer,12 and use it to obtain node voltage V2.Data from Problem 9.25For the network shown in Fig. 9-33, obtain the input
Obtain the Thévenin and Norton equivalent circuits at terminals ab for the network of Fig. 9-52. 3 Ω -j4 Ω + 10/45° V 20/0° V 10 Ω 5 Ω θα ob
Obtain the Thévenin and Norton equivalent circuits at terminals ab for the network of Fig. 9-53. १०- U S! oa US US! US 10 Ω 5/30° A
For the network of Problem 9.27, obtain a Norton equivalent circuit (Fig. 9-35).Data from Problem 9.27Replace the active network in Fig. 9-34(a) at terminals ab with a Thévenin equivalent. Z' O a ob
Replace the active network in Fig. 9-34(a) at terminals ab with a Thévenin equivalent. 9e - Ut! US! 30 I US + ) ()/(I
In the circuit of Fig. 9-54, v1 = 10 V and v2 = 5 sin 2000t. Find i. V1 +1 10 92 ww 5 mH ele +1 V2
Obtain the Thévenin equivalent for the bridge circuit of Fig. 9-36. Make V′ the voltage of a with respect to b. 20/0° VI + 21 Ω 12 Ω κα 124 Ω * b + 50 Ω 30 Ω j60 Ω
In the circuit of Fig. 9-55, v1 = 6 cos ωt and v2 = cos (ωt + 60°). Find vA if ω = 2 rad/sec. +1 H9 ele A 0.5 F HH 1 F 4 H 1₂ +1 V2
Replace the network of Fig. 9-37 at terminals ab with a Norton equivalent and with a Thévenin equivalent. 10 Ω 10/0° _V - -/10 Ω 3 Ω | j4 Ω
In the circuit of Problem 9.59 find phasor currents I1 and I2 drawn from the two sources.Data from Problem 9.59In the circuit of Fig. 9-55, v1 = 6 cos ωt and v2 = cos (ωt + 60°). Find vA if ω = 2
Find vA in the circuit of Problem 9.59 if ω = 0.5 rad/s.Data from Problem 9.59In the circuit of Fig. 9-55, v1 = 6 cos ωt and v2 = cos (ωt + 60°). Find vA if ω = 2 rad/sec. +1 H9 ele A 0.5 F HH 1
In the circuit of Fig. 9-55, v1 = V1 cos (0.5t + θ1) and v2 = V2 cos (0.5t + θ2). Find the current through the 4 H inductor. +1 6 H mor A 0.5 F HH 1 F 4 H 12 + V2
A series RLC circuit, with R = 200 Ω, L = 0.10 H, and C = 13.33 μF, has an initial charge on the capacitor of Q0 = 2.67 × 10−3 C. A switch is closed at t = 0, allowing the capacitor to
A series RLC circuit, with R = 3 kΩ, L = 10 H, and C = 200 μF, has a constant-voltage source, V = 50 V, applied at t =0. (a) Obtain the current transient, if the capacitor has no initial
Repeat Example 8.1 for C = 10 μF, which results in a = ω0.Data from Example 8.1A series RLC circuit, with R = 200 Ω, L = 0.10 H, and C = 13.33 μF, has an initial charge on the capacitor of Q0 =
A series RLC circuit, with R = 200 Ω, L = 0.1 H, and C = 100 μF, has a voltage source of 200 V applied at t = 0. Find the current transient, assuming zero initial charge on the capacitor.
A series RLC circuit, with R = 50 Ω, L = 0.1 H, and C = 50 μF, has a constant voltage V = 100 V applied at t = 0. Obtain the current transient, assuming zero initial charge on the capacitor.
Repeat Example 8.1 for C = 1 μF.Data from Example 8.1A series RLC circuit, with R = 200 Ω, L = 0.10 H, and C = 13.33 μF, has an initial charge on the capacitor of Q0 = 2.67 × 10−3 C. A switch
Rework Problem 8.2, if the capacitor has an initial charge Q0 = 2500 μC.Data from Problem 8.2A series RLC circuit, with R = 50 Ω, L = 0.1 H, and C = 50 μF, has a constant voltage V = 100 V applied
What value of capacitance, in place of the 100 μF in Problem 8.23, results in the critically damped case?Data from Problem 8.23A series RLC circuit, with R = 200 Ω, L = 0.1 H, and C = 100 μF, has
A parallel RLC network, with R = 50.0 Ω, C = 200 μF, and L = 55.6 mH, has an initial charge Q0 = 5.0 mC on the capacitor. Obtain the expression for the voltage across the network.
Find the natural resonant frequency, |β|, of a series RLC circuit with R = 200 Ω, L = 0.1 H, C = 5 μF.
In Fig. 8-19, the switch is closed at t = 0. Obtain the current i and capacitor voltage vC, for t > 0. 50 V U 10 Ω 10 Ω U U + Ve 2 μF
A parallel RLC circuit, with R = 1000 Ω, C = 0.167 μF, and L = 1.0 H, has an initial voltage V0 = 50.0 V on the capacitor. Obtain the voltage v(t) when the switch is closed at t = 0.
A parallel RLC circuit, with R = 200 Ω, L = 0.28 H, and C = 3.57 μF, has an initial voltage V0 = 50.0 V on the capacitor. Obtain the voltage function when the switch is closed at t = 0.
For the time functions listed in the first column of Table 8-2, write the corresponding amplitude and phase angle (cosine-based) and the complex frequency s.Data from Table 8-2 Time Function i(t) =
A voltage of 10 V is applied at t = 0 to a series RLC circuit with R = 5 Ω, L = 0.1 H, C = 500 μF. Find the transient voltage across the resistance.
A series RL circuit, with R = 10 Ω and L = 2 H, has an applied voltage v = 10 e−2t cos (10t + 30°).
In the two-mesh circuit shown in Fig. 8-31, the switch is closed at t = 0. Find i1 and i2, for t > 0. 50 V ( 1 ΣΩ Μ 20 με ἐξ 5Ω 0.1 Η
For each amplitude and phase angle in the first column and complex frequency s in the second column in Table 8-3, write the corresponding time function. A
A series RC circuit, with R = 10 Ω and C = 0.2 F, has the same applied voltage as in Example 8.6.
A passive network in the s-domain is shown in Fig. 8-13. Obtain the network function for the current I(s) due to an input voltage V(s). V(s) + I(s) 2.5 (2 20 S
A voltage has the s-domain representation 100 ∠30° V. Express the time function for(a) s = −2Np/s,(b) s = −1 + j5s−1.
The same network as in Example 8.8 is shown in Fig. 8-16. Obtain the natural response when a source V(s) is inserted at xx′.Data from Example 8.8A passive network in the s-domain is shown in Fig.
Test the response of the network of Example 8.8 to an exponential voltage excitation v = 1est, where s = 1 Np/s.
For the circuit shown in Fig. 8-20, obtain v at t = 0.1 s for source current(a) i = 10 cos 2t (A),(b) i = 10e−t cos 2t (A). Zin (s) = 2 + 2(s+2) s+4 = s+3 (4) s+4 -
A passive network contains resistors, a 70-mH inductor, and a 25-μF capacitor. Obtain the respective s-domain impedances for a driving voltage(a) v = 100 sin (300t + 45°) (V),(b) v = 100e−100t
Calculate the impedance Z(s) for the circuit shown in Fig. 8-32 at(a) s = 0,(b) s = j1 rad/s,(c) s = j2 rad/s,(d) |s| = ∞. s2 1Ω- 103 202
A phasor current 25 ∠40° A has complex frequency s = −2 + j3 s−1. What is the magnitude of i(t) at t = 0.2s?
The network of Fig. 8-16 is driven by current I(s) across terminals yy′. The network function is H(s) = V(s)/I(s) = Z(s). The three branches are in parallel so that H(s) Z(s) = = 1 1 S + 2.5+5s
Obtain the impedance Zin(s) for the circuit shown in Fig. 8-21 at(a) s = 0,(b) s = j4 rad/s,(c) |s| = ∞. Zin (s) = 2 + 2)s + 1) 2«+v(4) 2(s +1) + S || s²+3s +4 (2) 5 2 s+ + 2
The voltage source in the s-domain circuit shown in Fig. 8-33 has the time-domain expressionObtain io(t). v;(t) = 10e cos 2t (V)
Express Z(s) for the circuit shown in Fig. 8-17 and observe the resulting magnitude scaling. Z(s) = K Ls + m K (K_R). Cs K m KR+ Cs KR = K₂_[Ls + R KLs R(1/Cs) R+ (1/Cs) K m Cs
Express the impedance Z(s) of the parallel combination of L = 4 H and C = 1 F. At what frequencies s is this impedance zero or infinite?
The circuit shown in Fig. 8-22 has a voltage source connected at terminals ab. The response to the excitation is the input current. Obtain the appropriate network function H(s).
Find H(s) = V2/V1 in the circuit of Fig. 8-41 and show that the circuit becomes a noninverting integrator if and only if R1C1 = R2C2. 마 +1 R₂ 싸 싸 B R₁ C₂ 고
In the time domain, a series circuit of R, L, and C has an applied voltage vi and element voltages vR, vL, and vC.Obtain the voltage transfer functions(a) Vr(s)/Vi(s),(b) VC(s)/Vi(s).
Obtain the network function H(s) for the circuit shown in Fig. 8-34. The response is the voltage Vi(s). + 1Ω 1(s)( 4 )V,(s) - Μ το 100 6Ω sl
Obtain H(s) for the network shown in Fig. 8-23, where the excitation is the driving current I(s) and the response is the voltage at the input terminals. I(s) V(s) 2s a 동 ⑤ 2I(s)
Construct the s-plane plot for the transfer function of Problem 8.34. Evaluate H(j3) from the plot.Data from Problem 8.34Obtain the network function H(s) for the circuit shown in Fig. 8-34. The
The circuit of Fig. 8-42 is called an equal-component Sallen-Key circuit. Find H(s) = V2/V1 and convert it to a differential equation. 싸 R R C ㅏ C B ㅏ R₂ ww Ry + 1/2
For the two-port network shown in Fig. 8-24 find the values of R1, R2, and C, given that the voltage transfer function is H₁ (s) = V. (s) 0.2 V.(s) s² + 3s + 2 ||
In the circuit of Fig. 8-42 assume R = 2 kΩ, C = 10 nF, and R2 = R1. Find v2 if v1 = v(t). ww R R C ㅏ B ㅏ ey RI + 2
Construct the pole-zero plot for the transfer admittance functionIn factored form, I_(s) H(s) = V V.(s) s² + 2s +17 2 + 3s + 2
Obtain H(s) = Vi(s)/Ii(s) for the circuit shown in Fig. 8-36 and construct the pole-zero plot. V (s) +1 sl 1,(s) 0.5s 2s
Write the transfer function H(s) whose pole-zero plot is given in Fig. 8-38. H(s) -20 + j40 -40 joo, rad/s -20-j40 -10 σ, Np/s
Find conditions in the circuit of Fig. 8-42 for sustained oscillations in v2(t) (with zero input) and find the frequency of oscillations.

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