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engineering
electrical engineering
Fundamentals of Applied Electromagnetics 6th edition Fawwaz T. Ulaby, Eric Michielssen, Umberto Ravaioli - Solutions
Use Thevenin?s theorem to find vo(t), t > 0, in figure.
Use Thevenin?s theorem to find vo(t), t > 0, in the network shown in figure.
Use Thevenin?s theorem to find io(t), t > 0, in the network shown in figure.
Find io(t), t > 0, in the network shown infigure.
Find vo(t), t > 0, in the network shown in figure. Assume that the circuit has reached steady state at t = 0 ?.
Find vo(t), t > 0 in the circuit infigure.
Find io(t), t > 0, in the network shown infigure.
Find io(t), t > 0, in the network shown infigure.
Find io(t), t > 0 in the network infigure.
Find vo(t), t > 0, in the circuit infigure.
Find vo(t), t > 0, in the circuit shown infigure.
Find io(t), t > 0, in the network infigure.
Find io(t), t > 0, in the network infigure.
Find vo(t), for t > 0, in the network infigure.
Find vo(t), for t > 0, in the network infigure
Find vo(t), for t > 0, in the network infigure.
Find vo(t), for t > 0, in the network infigure.
Find vo(t), for t > 0, in the network infigure.
Find vo(t), for t > 0, in the network infigure.
Given the network in figure determine the value of the output voltage as t ? ?.
For the network shown in figure, determine the value of the output voltage as t ? ?.
Determine the initial and final values of the voltage vo(t) in the network infigure.
Determine the initial and final values of the voltage vo(t) in the network infigure.
Find the initial and final values of the current io(t) in the network infigure.
Determine the output voltage vo(t) in the network in figure a if the input is given by the source in figureb.
Determine the output voltage, vo(t), in the circuit in figure a if the input is given by the source described in figure b.
Find the output voltage, vo(t), t > 0 in the network in figure a if the input is represented by the waveform shown in figureb.
Find the transfer function Vo(s) / Vi(s) for the network shown infigure.
Determine the transfer function Io(s) / Ii(s) for the network shown infigure.
Find the transfer function for the network shown infigure.
Find the transfer function for the network shown infigure.
Find the transfer function for the network infigure.
Find the transfer function for the network infigure.
Find the transfer function for the network in figure. If a step function is applied to the network, will the response be over damped, under damped, or criticallydamped?
Determine the transfer function for the network shown in figure. If a step function is applied to the network, what type of damping will the networkexhibit?
The transfer function of the network is given by the expression. Determine the damping ratio, the un-damped natural frequency, and the type of response that will be exhibited by thenetwork.
The voltage response of the network to a unit step input is the response over damped?
The voltage response of a network to a unit step input is the response critically damped?
The transfer function of the network is given by the expression Determine the damping ratio, the un-damped natural frequency, and the type of response that will be exhibited by the network.
For the network in figure, choose the value of C for criticaldamping.
For the filter in figure, choose the values of C1 and C2 to place poles at s = ? 2 and s = ? 5 rad/s.
Find the steady-state response vo(t) for the circuit shown infigure.
Find the steady-state response vo(t) for the network infigure.
Determine the steady-state response vo(t) for the network infigure.
Determine the steady-state response io(t) for the network infigure.
Find the steady-state response io(t) for the network in shown infigure.
Find the steady-state response vo(t), t > 0, in the network infigure.
Find the steady-state response vo(t), t > 0, in the network infigure.
A single-loop, second-order circuit is described by the following differential equation.Which is the correct form of the total (natural plus forced) response?a. v(t) = K1 + K2e–t b. v(t) = K1 cos t + K2 sin tc. v(t) = K1 + K2te–t d. v(t) = K1 + K2e–t cos t + K3e–t sin t
If all initial conditions are zero in the network in figure, find the transfer function Vo(s) /Vs(s).
The initial conditions in the circuit in figure are zero. Find the transfer function Io(s) /Is(s).
In the circuit in figure, use Laplace transforms to find the current I(s). Assume zero initial conditions and that vs(t) = 4 cos tu(t).
Assuming that the initial inductor current is zero in the circuit in figure, find the transfer function Vo(s) /Vs(s).
Consider the red wave shown in Fig. E1.1. what is the wave's (a) amplitude, (b) wavelength, and (c) frequency, given that its phase velocity is 6 m/s?
A phasor voltage is given by V̅ = j5 V. Find v(t).
The wave shown in red in Fig. E1.2 is given by u = 5cos2pt=8. Of the following four equations:(1) υ = 5cos(2πt / 8 - π / 4),(2) υ = 5cos(2πt / 8 + π / 4),(3) υ = -5cos(2πt=8 / π / 4),(4) υ
The electric field of a traveling electromagnetic wave is given by E (z, t) = 10cos (π × 10-7t + πz / 15 + π / 6) (V/m): Determine (a) the direction of wave propagation, (b) the wave frequency f, (c) its wavelength l, and (d) its phase velocity up.
Consider the red wave shown in Fig. E1.4. what is the wave's (a) amplitude (at x = 0), (b) wavelength, and (c) attenuation constant?
The red wave shown in Fig. E1.5 is given by u = 5cos4px (V). What expression is applicable to (a) the blue wave and (b) the green wave?
An electromagnetic wave is propagating in the z-direction in a lossy medium with attenuation constant α = 0:5 Np/m. If the wave's electric-field amplitude is 100 V/m at z = 0, how far can the wave travel before its amplitude will have been reduced to (a) 10 V/m, (b) 1 V/m, (c) 1 mV/m?
Express the following complex functions in polar form: z1 = (4 - j3)2, z2 = (4 - j3)1/2.
Show that √2 j = ± (1 + j).
A series RL circuit is connected to a voltage source given by vs(t) = 150coswt (V). Find (a) the phasor current I and (b) the instantaneous current i(t) for R = 400 Ω, L = 3 mH, and ( = 105 rad/s.
Use Table 2-1 to compute the line parameters of a two-wire air line whose wires are separated by a distance of 2 cm, and each is 1 mm in radius. The wires may be treated as perfect conductors with σc = ∞.
If Г = 0.5 and λ = 24cm, find the locations of the voltage maximum and minimum nearest to the load.
A 140-Ω lossless line is terminated in a load impedance ZL = (280 + j182) Ω. If λ = 72 cm, find (a) the reflection coefficient Г, (b) the voltage standing-wave ratio S, (c) the locations of voltage maxima, and (d) the locations of voltage minima.
A 50-Ω lossless transmission line uses an insulating material with εr = 2:25. When terminated in an open circuit, how long should the line be for its input impedance to be equivalent to a 10-pF capacitor at 50 MHz?
A 300-Ω feedline is to be connected to a 3-m long, 150- Ω line terminated in a 150- Ω resistor. Both lines are lossless and use air as the insulating material, and the operating frequency is 50 MHz. Determine (a) The input impedance of the 3-m long line, (b) The voltage standing-wave ratio on
For a 50-Ω lossless transmission line terminated in a load impedance ZL = (100 + j50) Ω, determine the fraction of the average incident power reflected by the load.
Use the Smith chart to find the values of Г corresponding to the following normalized load impedances: (a) zL = 2 + j0, (b) zL = 1- j1, (c) zL = 0.5 - j2, (d) zL = - j3, (e) zL = 0 (short circuit), (f) zL = ∞ (open circuit), (g) zL = 1 (matched load).
Use the Smith chart to find the normalized input impedance of a lossless line of length l terminated in a normalized load impedance zL for each of the following combinations: (a) l = 0.25λ, zL = 1 + j0, (b) l = 0.5λ, zL = 1+ j1, (c) l = 0.3λ, zL = 1 - j1, (d) l =1.2λ, zL = 0.5 - j0.5, (e) l =
Calculate the transmission line parameters at 1 MHz for a rigid coaxial air line with an inner conductor diameter of 0.6 cm and an outer conductor diameter of 1.2 cm. The conductors are made of copper [see Appendix B for mc and μc of copper].
Verify that Eq. (2.26a) is indeed a solution of the wave equation given by Eq. (2.21).
A two-wire air line has the following line parameters: R' = 0.404 (mΩ/m), L0 = 2.0 (μH/m), G' = 0, and C' = 5.56 (pF/m). For operation at 5 kHz, determine (a) the attenuation constant a, (b) the phase constant b, (c) the phase velocity up, and (d) the characteristic impedance Z0.
A lossless transmission line uses a dielectric insulating material with εr = 4. If its line capacitance is C' =10 (pF/m), find (a) the phase velocity μp, (b) the line inductance L', and (c) the characteristic impedance Z0.
Use CD Module 2.4 to generate the voltage and current standing-wave patterns for a 50-Ω line of length 1.5l, terminated in an inductance with ZL = j140 Ω.
Find the distance vector between P1(1, 2,3) and P2(-1, - 2, 3) in Cartesian coordinates.
Find the directional derivative of V = rz2 cosϕ along the direction A= 2 - and evaluate it at (1, π / 2, 2).
The power density radiated by a star [Fig. E3.11(a)] decreases radially as S(R) = S0 / R2, where R is the radial distance from the star and S0 is a constant. Recalling that the gradient of a scalar function denotes the maximum rate of change of that function per unit distance and the direction of
The graph in Fig. E3.12(a) depicts a gentle change in atmospheric temperature from T1 over the sea to T2 over land. The temperature profile is described by the functionT(x) = T1 + (T2 - T1) = (e-x + 1),Where x is measured in kilometers and x = 0 is the sea-land boundary. (a) In which direction does
Given A = e-2y(sin2x+ cos2x), find ▽A.
Given A = r cos ϕ + r sin ϕ + 3z, find ▽∙ A at (2, 0, 3).
If E = AR in spherical coordinates, calculate the flux of E through a spherical surface of radius a, centered at the origin.
Verify the divergence theorem by calculating the volume integral of the divergence of the field E of Exercise 3.11 over the volume bounded by the surface of radius a.
The arrow representation in Fig. E3.17 represents the vector field A = - y. At a given point in space, A has a positive divergence –½ ˆ™ A if the net flux flowing outward through the surface of an imaginary infinitesimal volume centered at that point is positive,
Find ▽ × A at (2, 0, 3) in cylindrical coordinates for the vector field A = 10e-2r cos ϕ + 10 sin ϕ.
Find ▽ × A = at (3, π / 6, 0) in spherical coordinated for the vector field
Find the angle q between vectors A and B of Example 3-1 using the cross product between them.
Find the angle that vector B of Example 3-1 makes with the z-axis.
Vectors A and B lie in the y-z plane and both have the same magnitude of 2 (Fig. E3.4). Determine(a) A ˆ™ B and(b) A × B
If A ∙ B = A ∙ C, does it follow that B = C?
A circular cylinder of radius r = 5 cm is concentric with the z-axis and extends between z = -3 cm and z = 3 cm. Use Eq. (3.44) to find the cylinder's volume.
Point P = (2√3, π / 3, -2) is given in cylindrical coordinates. Express p in spherical coordinates.
Transform vector A = (x + y) + (y - x) + z From Cartesian to cylindrical coordinates.
Given V = x2y + xy2 + xz2,(a) Find the gradient of V, and(b) Evaluate it at (1, -1, 2).
A square plate in the x-y plane is situated in the space defined by -3 m ≤ x ≤ 3 m and -3 m ≤ y ≤ 3 m. Find the total charge on the plate if the surface charge density is given by ps = 4y2 (μC/m2).
Determine the electric potential at the origin due to four 20-μC charges residing in free space at the corners of a 2 m × 2 m square centered about the origin in the x-y plane.
A spherical shell of radius R has a uniform surface charge density (s. Determine the electric potential at the center of the shell.
Determine the density of free electrons in aluminum, given that its conductivity is 3.5 × 107 (S/m) and its electron mobility is 0.0015 (m2/V∙ s).
The current flowing through a 100-m-long conducting wire of uniform cross section has a density of 3 × 105 (A/m2). Find the voltage drop across the length of the wire if the wire material has a conductivity of 2 × 107 (S/m).
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