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electrical engineering

Questions and Answers of Electrical Engineering

The magnetic field of a plane wave traveling in air is given by H = x50sin (2x 107t) ky (mA/m). Determine the average power density carried by the wave.
A wave traveling in a nonmagnetic medium with r = 9 is characterized by an electric field given byDetermine the direction of wave travel and the average power density carried by the wave.
The electric-field phasor of a uniform plane wave traveling downward in water is given byWhere zË† is the downward direction and z = 0 is the water surface. If
The amplitudes of an elliptically polarized plane wave traveling in a lossless, nonmagnetic medium with r = 4 are Hy0 = 3 (mA/m) and Hz0 = 4 (mA/m). Determine the average power flowing
A wave traveling in a lossless, nonmagnetic medium has an electric field amplitude of 24.56 V/m and an average power density of 2.4 W/m2. Determine the phase velocity of the wave.
At microwave frequencies, the power density considered safe for human exposure is 1 (mW/cm2). A radar radiates a wave with an electric field amplitude E that decays with distance as E (R, = (3, 000,
Consider the imaginary rectangular box shown in Fig. 7-19 (P7.31).(a) Determine the net power flux P (t) entering the box due to a plane wave in air given by(b) Determine the net time-average power
Repeat Problem 7.31 for a wave traveling in a lossy medium in whichThe box has dimensions A =1 cm, b =2 cm, and c =0.5 cm.
Given a wave with E = xE0cos (wt €“ kz) Calculate:(a) The time-average electric energy density(b) The time-average magnetic energy density (wm)av = 1/T f wm dt = 1/2T f μH2 dt, and(c)
A 60-MHz plane wave traveling in the – x-direction in dry soil with relative permittivity r = 4 has an electric field polarized along the z-direction. Assuming dry soil to be approximately
At 2 GHz, the conductivity of meat is on the order of 1 (S/m). When a material is placed inside a microwave oven and the field is activated, the presence of the electromagnetic fields in the
A team of scientists is designing a radar as a probe for measuring the depth of the ice layer over the Antarctic land mass. In order to measure a detectable echo due to the reflection by the ice-rock
A plane wave in air with an electric field amplitude of 20 V/m is incident normally upon the surface of a lossless, nonmagnetic medium with r = 25. Determine: (a) The reflection and
A plane wave traveling in medium 1 with r1 = 2:25 is normally incident upon medium 2 with r2 = 4. Both media are made of nonmagnetic, non-conducting materials. If the electric field of the incident
A plane wave traveling in a medium with r1 = 9 is normally incident upon a second medium with r2 = 4. Both media are made of nonmagnetic, non-conducting materials. If the magnetic field of the
A 200-MHz left-hand circularly polarized plane wave with an electric field modulus of 5 V/m is normally incident in air upon a dielectric medium with r = 4 and occupying the region defined by
Repeat Problem 8.4 after replacing the dielectric medium with a poor conductor characterized by r = 2:25, μr = 1, and = 10–4 S/m.
A 50-MHz plane wave with electric field amplitude of 50 V/m is normally incident in air onto a semi-infinite, perfect dielectric medium with r = 36. Determine (a) , (b) The
What is the maximum amplitude of the total electric field in the air medium of Problem 8.6, and at what nearest distance from the boundary does it occur?
Repeat Problem 8.6 after replacing the dielectric medium with a conductor with r = 1, μr = 1, and = 2:78 x 10–3 S/m
For some types of glass, the index of refraction varies with wavelength. A prism made of a material with where 0 is the wavelength in vacuum, was used to disperse white light as shown in Fig.
The two prisms in Fig. 8-35 (P8.19) are made of glass with n = 1:5. What fraction of the power density carried by the ray incident upon the top prism emerges from bottom prism? Neglect multiple
The three regions shown in Fig. 8-32 (P8.9) contain perfect dielectrics. For a wave in medium 1 incident normally upon the boundary at z = - d, what combination of r2 and d produce no
For the configuration shown in Fig. 8-32 (P8.9), use transmission line equations (or the Smith chart) to calculate the input impedance at z = - d for r1 = 1, r2 = 9, r3 = 4, d
Repeat Problem 8.10 after interchanging r1 and r3.
Orange light of wavelength 0.61 μm in air enters a block of glass with r = 1:44. What color would it appear to a sensor embedded in the glass? The wavelength ranges of colors are violet
A plane wave of unknown frequency is normally incident in air upon the surface of a perfect conductor. Using an electric-field meter, it was determined that the total electric field in the air medium
Consider a thin film of soap in air under illumination by yellow light with = 0:6 μm in vacuum. If the film is treated as a planar dielectric slab with r = 1:72,
A 5-MHz plane wave with electric field amplitude of 10 (V/m) is normally incident in air onto the plane surface of a semi-infinite conducting material with r = 4, μr = 1, and
A 0.5-MHz antenna carried by an airplane flying over the ocean surface generates a wave that approaches the water surface in the form of a normally incident plane wave with an electric-field
A light ray is incident on a prism at an angle as shown in Fig. 8-33 (P8.17). The ray is refracted at the first surface and again at the second surface. In terms of the apex angleof the prism
Figure P8.21 depicts a beaker containing a block of glass on the bottom and water over it. The glass block contains a small air bubble at an unknown depth below the water surface. When viewed from
A glass semi cylinder with n = 1:5 is positioned such that its flat face is horizontal, as shown in Fig. 8-38 (P8.22). Its horizontal surface supports a drop of oil, as shown. When light is directed
A penny lies at the bottom of a water fountain at a depth of 30 cm. Determine the diameter of a piece of paper which, if placed to float on the surface of the water directly above the penny, would
Suppose the optical fiber of Example 8-5 is submerged in water (with n = 1:33) instead of air. Determine a and fp in that case.
Equation (8.45) was derived for the case where the light incident upon the sending end of the optical fiber extends over the entire acceptance cone shown in Fig. 8-12(b). Suppose the incident light
A plane wave in air withIs incident upon the planar surface of a dielectric material, with r = 4, occupying the half space z _ 0. Determine:(a) The polarization of the incident wave,(b) The
Repeat Problem 8.26 for a wave in air withIncident upon the planar boundary of a dielectric medium (z _ 0) with r = 9.
Natural light is randomly polarized, which means that, on average, half the light energy is polarized along any given direction (in the plane orthogonal to the direction of propagation) and the other
A parallel polarized plane wave is incident from air onto a dielectric medium with r = 9 at the Brewster angle. What is the refraction angle?
A perpendicularly polarized wave in air is obliquely incident upon a planar glass-air interface at an incidence angle of 30_. The wave frequency is 600 THz (1 THz = 1012 Hz), which corresponds to
Show that the reflection coefficient can be written in the form.
Show that for nonmagnetic media, the reflection coefficient k can be written in the form.
A parallel polarized beam of light with an electric field amplitude of 10 (V/m) is incident in air on polystyrene with μr = 1 and r = 2:6. If the incidence angle at the air–polystyrene
Derive Eq. (8.89b).
A hollow rectangular waveguide is to be used to transmit signals at a carrier frequency of 6 GHz. Choose its dimensions so that the cutoff frequency of the dominant TE mode is lower than the carrier
A TE wave propagating in a dielectric-filled waveguide of unknown permittivity has dimensions a= 5 cm and b=3 cm. If the x-component of its electric field is given byDetermine:(a) The mode number,(b)
A waveguide filled with a material whose r = 2:25 has dimensions a = 2 cm and b = 1:4 cm. If the guide is to transmit 10.5-GHz signals, what possible modes can be used for the transmission?
For a rectangular waveguide operating in the TE10 mode, obtain expressions for the surface charge density s and surface current density Js on each of the four walls of the guide.
A waveguide, with dimensions a = 1 cm and b = 0:7 cm, is to be used at 20 GHz. Determine the wave impedance for the dominant mode when (a) The guide is empty, and (b) The guide is filled with
A narrow rectangular pulse superimposed on a carrier with a frequency of 9.5 GHz was used to excite all possible modes in a hollow guide with a = 3 cm and b = 2:0 cm. If the guide is 100 m in length,
If the zigzag angle 0 is 42_ for the TE10 mode, what would it be for the TE20 mode?
Measurement of the TE101 frequency response of an air-filled cubic cavity revealed that its Q is 4802. If its volume is 64 mm3, what material are its sides made of?
A hollow cavity made of aluminum has dimensions a = 4 cm and d = 3 cm. Calculate Q of the TE101 mode for(a) b = 2 cm, and(b) b = 3 cm
A 50-MHz right-hand circularly polarized plane wave with an electric field modulus of 30 V/m is normally incident in air upon a dielectric medium with r = 9 and occupying the region defined
Consider a flat 5-mm-thick slab of glass with r = 2:56. (a) If a beam of green light (0 = 0:52 μm) is normally incident upon one of the sides of the slab, what percentage of the incident power
A parallel-polarized plane wave is incident from air at an angle thetai = 30_ onto a pair of dielectric layers as shown in the figure.(a) Determine the angles of transmission theta2, theta3, and
A plane wave in air withis incident upon the planar surface of a dielectric material, with Er = 2:25, occupying the half-space z _ 0. Determine(a) The incidence angle thetai.(b) The frequency of the
A center-fed Hertzian dipole is excited by a current I0 = 20 A. If the dipole is 50 in length, determine the maximum radiated power density at a distance of 1 km
A 1-m-long dipole is excited by a 1-MHz current with an amplitude of 12 A. What is the average power density radiated by the dipole at a distance of 5 km in a direction that is 45o from the dipole
Determine the(a) Direction of maximum radiation,(b) Directivity,(c) Beam solid angle, and(d) Half-power beam width in the x€“z plane for an antenna whose normalized radiation intensity is
Repeat Problem 9.3 for an antenna with
A 2-m-long center-fed dipole antenna operates in the AM broadcast band at 1 MHz. The dipole is made of copper wire with a radius of 1 mm.(a) Determine the radiation efficiency of the antenna.(b) What
Repeat Problem 9.5 for a 20-cm-long antenna operating at 5 MHz.
An antenna with a pattern solid angle of 1.5 (sr) radiates 60 W of power. At a range of 1 km, what is the maximum power density radiated by the antenna?
An antenna with a radiation efficiency of 90% has a directivity of 7.0 dB. What is its gain in dB?
The radiation pattern of a circular parabolic-reflector antenna consists of a circular major lobe with a half-power beam width of 3 and a few minor lobes. Ignoring the minor lobes, obtain an estimate
The normalized radiation intensity of a certain antenna is given by F(q)= exp (20q2) for 0 (a) The half-power beam width,(b) The pattern solid angle,(c) The antenna directivity.
Repeat Problem 9.5 for a 1-m-long half-wave dipole that operates in the FM/TV broadcast band at 150 MHz.
Assuming the loss resistance of a half-wave dipole antenna to be negligibly small and ignoring the reactance component of its antenna impedance, calculate the standing wave ratio on a
For the short dipole with length l such that lAs shown in Fig. 9-36 (P9.13). Use this current distribution to determine(a) The far-field E (R, ),(b) The power density
For a dipole antenna of length l =32, (a) Determine the directions of maximum radiation, (b) Obtain an expression for Smax, and (c) Generate a plot of the normalized radiation pattern
Repeat parts (a)–(c) of Problem 9.14 for a dipole of length l = 3l/4.
Repeat parts (a)–(c) of Problem 9.14 for a dipole of length l = ..
A car antenna is a vertical monopole over a conducting surface. Repeat Problem 9.5 for a 1-m-long car antenna operating at 1 MHz. The antenna wire is made of aluminum with μc = μ0 and sc =
Determine the effective area of a half-wave dipole antenna at 100 MHz, and compare it to its physical cross section if the wire diameter is 2 cm.
A 3-GHz line-of-sight microwave communication link consists of two lossless parabolic dish antennas, each 1 m in diameter. If the receive antenna requires 10 nW of receive power for good reception
A half-wave dipole TV broadcast antenna transmits 1 kW at 50MHz. What is the power received by a home television antenna with 3-dB gain if located at a distance of 30 km?
A 150-MHz communication link consists of two vertical half-wave dipole antennas separated by 2 km. The antennas are lossless, the signal occupies a bandwidth of 3 MHz, the system noise temperature of
Consider the communication system shown in Fig. 9-37 (P9.22), with all components properly matched. If Pt = 10 W and f =6 GHz:(a) What is the power density at the receiving antenna (assuming proper
A uniformly illuminated aperture is of length lx = 20 Determine the beam width between first nulls in the x–z plane.
A uniformly illuminated rectangular aperture situated in the x–y plane is 2 m high (along x) and 1 m wide (along y). If f = 10 GHz, determine(a) The beam widths of the radiation pattern in the
An antenna with a circular aperture has a circular beam with a beam width of 3 =at 20 GHz.(a) What is the antenna directivity in dB?(b) If the antenna area is doubled, what would be the new
The 10-dB beam width is the beam size between the angles at which F () is 10 dB below its peak value. Determine the 10-dB beam width in the x–z plane for a uniformly illuminated aperture
A 94-GHz automobile collision-avoidance radar uses a rectangular aperture antenna placed above the car’s bumper. If the antenna is 1 m in length and 10 cm in height,(a) What are its elevation and
A microwave telescope consisting of a very sensitive receiver connected to a 100-m parabolic-dish antenna is used to measure the energy radiated by astronomical objects at 20 GHz. If the antenna beam
A two-element array consisting of two isotropic antennas separated by a distance d along the z-axis is placed in a coordinate system whose z-axis points eastward and whose x-axis points toward the
If the antennas in part(a) of Problem 9.29 are parallel vertical Hertzian dipoles with axes along the x-direction, determine the normalized radiation intensity in the x-z plane and plot it.
Consider the two-element dipole array of Fig. 9.29(a). If the two dipoles are excited with identical feeding coefficients (a0 = a1 = 1 and 0 = 1 = 0), choose
Choose (d/) so that the array pattern of the array of Problem 9.31 has a null, rather than a maximum, at 45o.
Find and plot the normalized array factor and determine the half power beam width for a five-element linear array excited with equal phase and a uniform amplitude distribution. The interelement
A three-element linear array of isotropic sources aligned along the zaxis has an interelement spacing of 4 Fig. 9-38 (P9.34). The amplitude excitation of the center element is twice
An eight-element linear array with 2 spacing is excited with equal amplitudes. To steer the main beam to a direction 60o below the broadside direction, what should be the incremental phase delay
A linear array arranged along the z-axis consists of 12 equally spaced elements with d =2. Choose an appropriate incremental phase delay so as to steer the main beam
A 50-cm long dipole is excited by a sinusoidally varying current with an amplitude I0 = 5 A. Determine the time average power radiated by the dipole if the oscillating frequency is:(a) 1 MHz,(b) 300
The configuration shown in the figure depicts two vertically oriented half-wave dipole antennas pointed towards each other, with both positioned on 100- m-tall towers separated by a distance of 5 km.
The figure depicts a half-wave dipole connected to a generator through a matched transmission line. The directivity of the dipole can be modified by placing a reflecting rod a distance d behind the
A five-element equally spaced linear array with d = 2 is excited with uniform phase and an amplitude distribution given by the binomial distributionWhere N is the
A remote sensing satellite is in circular orbit around the earth at an altitude of 1,100 km above the earth’s surface. What is its orbital period?
A transponder with a bandwidth of 400 MHz uses polarization diversity. If the bandwidth allocated to transmit a single telephone channel is 4 kHz, how many telephone channels can be carried by the

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