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electrical engineering

Questions and Answers of Electrical Engineering

A 50-m-long copper wire has a circular cross section with radius r = 2 cm. Given that the conductivity of copper is 5.8 × 107 (S/m), determine (a) The resistance R of the wire and (b) The power
Repeat part (b) of Exercise 4.14 by applying Eq. (4.80).In Exercise 4.14The power dissipated in the wire if the voltage across its length is 1.5 (mV).
Find E1 in Fig. 4-19 if E2 = 2 - 3 + 3 (V/m), Îµ1 = 2Îµ0, Îµ2 = 8Îµ0, and the boundary is charge free.
Repeat Exercise 4.16 for a boundary with surface charge density (s = 3.54 Ã— 10-11 (C/m2).
The radii of the inner and outer conductors of a coaxial cable are 2 cm and 5 cm, respectively, and the insulating material between them has a relative permittivity of 4. The charge density on the
Use the result of Example 4-13 to find the surface charge density (S on the surface of the conducting plane.
A spherical shell centered at the origin extends between R = 2 cm and R = 3 cm. If the volume charge density is given by (v = 3R × 10-4 (C/m3), find the total charge contained in the shell.
Four charges of 10 μC each are located in free space at points with Cartesian coordinates (-3, 0, 0), (3, 0, 0), (0, -3, 0), and (0, 3, 0). Find the force on a 20-μC charge located at (0, 0, 4).
Two identical charges are located on the x-axis at x = 3 and x = 7. At what point in space is the net electric field zero?
In a hydrogen atom the electron and proton are separated by an average distance of 5.3 × 10-11 m. Find the magnitude of the electrical force Fe between the two particles, and compare it with the
An infinite sheet of charge with uniform surface charge density rs is located at z = 0 (x-y plane), and another infinite sheet with density -(s is located at z = 2 m, both in free space. Determine E
Two infinite lines of charge, each carrying a charge density (l, are parallel to the z-axis and located at x = 1 and x = -1. Determine E at an arbitrary point in free space along the y-axis.
A thin spherical shell of radius a carries a uniform surface charge density (s. Use Gauss's law to determine E.
A spherical volume of radius a contains a uniform volume charge density (v. Use Gauss's law to determine D for (a) R ≥ a and (b) R ≥ a.
An electron moving in the positive x-direction perpendicular to a magnetic field experiences a deflection in the negative z-direction. What is the direction of the magnetic field?
The metal niobium becomes a superconductor with zero electrical resistance when it is cooled to below 9 K, but its superconductive behavior ceases when the magnetic flux density at its surface
The magnetic vector M is the vector sum of the magnetic moments of all the atoms contained in a unit volume (1m3). If a certain type of iron with 8.5 ×1028 atoms/m3 contributes one electron per atom
With reference to Fig. 5-24, determine the angle between H1 and 2 = if H2 = (3 + 2) (A/m), Î¼r1 = 2, and Î¼r2 = 8, and Js = 0.
Use Eq. (5.89) to obtain an expression for B at a point on the axis of a very long solenoid but situated at its end points. How does B at the end points compare to B at the midpoint of the solenoid?
A proton moving with a speed of 2 × 106 m/s through a magnetic field with magnetic flux density of 2.5 T experiences a magnetic force of magnitude 4 × 10-13 N. What is the angle between the
A charged particle with velocity u is moving in a medium containing uniform fields E = E and B = B. What should u be so that the particle experiences no net force on it?
A horizontal wire with a mass per unit length of 0.2 kg/m carries a current of 4 A in the +x-direction. If the wire is placed in a uniform magnetic flux density B, what should the direction and
A semiinfinite linear conductor extends between z = 0 and z = ˆž along the z-axis. If the current I in the conductor flows along the positive z-direction, find H at a point in the x-y plane
A wire carrying a current of 4 A is formed into a circular loop. If the magnetic field at the center of the loop is 20 A/m, what is the radius of the loop if the loop has (a) Only one turn and (b) 10
A wire is formed into a square loop and placed in the x-y plane with its center at the origin and each of its sides parallel to either the x- or y-axes. Each side is 40 cm in length, and the wire
For the loop shown in Fig. 6-3, what is Vtremf if B = B0 cos (t?
Suppose that the loop of Example 6-1 is replaced with a 10-turn square loop centered at the origin and having 20-cm sides oriented parallel to the x- and y-axes. If B = B0x2 cos 103t and B0 = 100 T,
For the moving loop of Fig. 6-9, find I when the loop sides are at y1 = 4 m and y2 = 4.5 m. Also, reverse the direction of motion such that u = -5 (m/s).
A poor conductor is characterized by a conductivity σ = 100 (S/m) and permittivity ε = 4 ε0. At what angular frequency ( is the amplitude of the conduction current density J equal to the amplitude
Determine(a) The relaxation time constant and(b) The time it takes for a charge density to decay to 1% of its initial value in quartz, given that εr = 5 and σ = 10-17 S/m.
The magnetic field intensity of an electromagnetic wave propagating in a lossless medium with Îµ = 9Îµ0 and Î¼ = Î¼0 is given byFind E(z, t) and k.
A 10-MHz uniform plane wave is traveling in a nonmagnetic medium with μ = μ0 and εr = 9. Find (a) The phase velocity, (b) The wave number, (c) The wavelength in the medium, and (d) The intrinsic
Convert the following values of the power ratio G to decibels: (a) 2.3, (b) 4 × 103, (c) 3 ×10-2.
Find the voltage ratio g in natural units corresponding to the following decibel values of the power ratio G: (a) 23 dB, (b) -14 dB, (c) -3.6 dB.
The electric field phasor of a uniform plane wave traveling in a lossless medium with an intrinsic impedance of 188.5 Î© is given byDetermine (a) The associated magnetic field phasor and(b) The
If the magnetic field phasor of a plane wave traveling in a medium with intrinsic impedance ( = 100 Î© is given byFind the associated electric field phasor.
Repeat Exercise 7.3 for a magnetic field given by
The electric field of a plane wave is given byE(z,t) = 3 cos ((t - kz) + 4 cos ((t - kz) (V/m).Determine(a) The polarization state,(b) The modulus of E, and(c) The inclination angle.
If the electric field phasor of a TEM wave is given bydetermine the polarization state.
The constitutive parameters of copper are μ = μ0 = 4π × 10-7 (H / m), ε = ε0 ~ (1 / 36π) × 10-9 (F / m), and σ = 5.8 × 107 (S / m). Assuming that these parameters are frequency independent,
Over what frequency range may dry soil, with εr =3, μr =1, and σ =10-4 (S/m), be regarded as a low-loss dielectric medium?
For a wave traveling in a medium with a skin depth (s, what is the amplitude of E at a distance of 3(s compared with its initial value?
To eliminate reflections of normally incident plane waves, a dielectric slab of thickness d and relative permittivity er2 is to be inserted between two semi-infinite media with relative
What is the cutoff frequency for the dominant TM mode in a waveguide filled with a material with εr = 4? The waveguide dimensions are a = 2b = 5 cm.
What are the values for (a) up, (b) ug, and (c) the zigzag angle θ' at f = 2f10 for a TE10 mode in a hollow waveguide?
Express the normal-incidence reflection coefficient at the boundary between two nonmagnetic, conducting media in terms of their complex permittivities.
Obtain expressions for the average power densities in media 1 and 2 for the fields described by Eqs. (8.22a) through (8.23b), assuming medium 1 is slightly lossy with (c1 approximately real.
If the light source of Exercise 8.4 is situated at a depth of 1 m below the water surface and if its beam is isotropic (radiates in all directions), how large a circle would it illuminate when
If the index of refraction of the cladding material in Example 8-5 is increased to 1.50, what would be the new maximum usable data rate?
A wave in air is incident upon a soil surface at Î¸i = 50o. If soil has Îµr = 4 and Î¼r = 1, determine
Show that the incident, reflected, and transmitted electric and magnetic fields given by Eqs. (8.65a) through (8.65f) all have the same exponential phase function along the x-direction.
A 1-m-long dipole is excited by a 5-MHz current with an amplitude of 5 A. At a distance of 2 km, what is the power density radiated by the antenna along its broadside direction?
The effective area of a parabolic dish antenna is approximately equal to its physical aperture. If the directivity of a dish antenna is 30 dB at 10 GHz, what is its effective area? If the frequency
With its bore sight direction along z, a square aperture was observed to have half-power beam widths of 3o in the both x-z and y-z planes. Determine its directivity in decibels.
What condition must be satisfied in order to use scalar diffraction to compute the field radiated by an aperture antenna? Can we use it to compute the directional pattern of the eye's pupilin the
Derive an expression for the array factor of a two-element array excited in phase with a0 = 1 and a1 = 3. The elements are positioned along the z-axis and are separated by λ / 2.
An equally spaced N-element array arranged along the z-axis is fed with equal amplitudes and phases; that is, Ai = 1 for i = 0, 1, ....., N - 1. What is the magnitude of the array factor in the
An antenna has a conical radiation pattern with a normalized radiation intensity F (θ) = 1 for θ between 0o and 45o and zero intensity for θ between 45o and 180o. The pattern is independent of the
The maximum power density radiated by a short dipole at a distance of 1 km is 60 (nW/m2). If I0 = 10 A, find the radiation resistance.
For the half-wave dipole antenna, evaluate F (θ) versus q in order to determine the half-power beam width in the elevation plane (the plane containing the dipole axis).
If the maximum power density radiated by a half-wave dipole is 50 (μW/m2) at a range of 1 km, what is the current amplitude I0?
The effective area of an antenna is 9 m2. What is its directivity in decibels at 3 GHz?
At 100 MHz, the pattern solid angle of an antenna is 1.3 sr. Find (a) The antenna directivity D and (b) its effective area Ae.
If the operating frequency of the communication system described in Example 9-4 is doubled to 12 GHz, what would then be the minimum required diameter of a home receiving TV antenna?
A 3-GHz microwave link consists of two identical antennas each with a gain of 30 dB. Determine the received power, given that the transmitter output power is 1 kW and the two antennas are 10 km apart.
Sketch the atomic structure of copper and discuss why it is a good conductor and how its structure is different from that of germanium, silicon, and gallium arsenide.
Using Eq. (1.1), determine the diode current at 20°C for a silicon diode with Is - 50 nA and an applied forward bias of 0.6 V.
Repeat Problem 15 for T = 100°C (boiling point of water). Assume that I, has increased to 5.0 p,A. In Problem 15 Using Eq. (1.1), determine the diode current at 20°C for a silicon diode with Is -
a. Using Eq. (1.1), determine the diode current at 20°C for a silicon diode with ls = 0.1 μA at a reverse-bias potential of -10 V. b. Is the result expected? Why?
a. Plot the function y = ex for x from 0 to 10. Why is it difficult to plot? b. What is the value of y = ex at x = 0? c. Based on the results of part (b), why is the factor -1 important in Eq. (1.1)?
In the reverse-bias region the saturation current of a silicon diode is about 0.1 μA (T = 20°C). Determine its approximate value if the temperature is increased 40°C.
In your own words, define an intrinsic material, a negative temperature coefficient, and covalent bonding.
Compare the characteristics of a silicon and a germanium diode and determine which you would prefer to use for most practical applications. Give some details. Refer to a manufacturer's listing and
Determine the forward voltage drop across the diode whose characteristics appear in Fig. 1.19 at temperatures of -75°C, 25°C, I25°C and a current of 10 mA. For each temperature, determine the
Describe in your own words the meaning of the word ideal as applied to a device or a system.
Describe in your own words the characteristics of the ideal diode and how they determine the on and off states of the device. That is, describe why the short-circuit and open-circuit equivalents are
What is the one important difference between the characteristics of a simple switch and those of an ideal diode?
Determine the static or dc resistance of the commercially available diode of Fig. 1.15 at a forward current of 2 mA.
Repeat Problem 25 at a forward current of 15 mA and compare results.
Determine the static or dc resistance of the commercially available diode of Fig. 1.15 at a reverse voltage of -10 V. How does it compare to the value determined at a reverse voltage of -30 V?
a. Determine the dynamic (ac) resistance of the diode of Fig. 1.27 at a forward current of 10 mA using Eq. (1.4). b. Determine the dynamic (ac) resistance of the diode of Fig. 1.27 at a forward
Calculate the dc and ac resistances for the diode of Fig. 1.27 at a forward current of 10 mA and compare their magnitudes.
Using Eq. (1.4), determine the ac resistance at a current of 1 mA and 15 mA for the diode of Fig. 1.27. Compare the solutions and develop a general conclusion regarding the ac resistance and
Using Eq. (1.5), determine the ac resistance at a current of 1 mA and 15 mA for the diode of Fig. 1.15. Modify the equation as necessary for low levels of diode current. Compare to the solutions
Determine the ac resistance for the diode of Fig. 1.15 at 0.75 V and compare it to the average ac resistance obtained in Problem 32.
Find the piecewise-linear equivalent circuit for the diode of Fig. 1.15. Use a straight-line segment that intersects the horizontal axis at 0.7 V and best approximates the curve for the region
Repeat Problem 34 for the diode of Fig. 1.27. In Problem 34 Use a straight-line segment that intersects the horizontal axis at 0.7 V and best approximates the curve for the region greater than 0.7 V.
a. Referring to Fig. 1.33, determine the transition capacitance at reverse-bias potentials of -25 V and -10 V. What is the ratio of the change in capacitance to the change in voltage? b. Repeat part
Referring to Fig. 1.33, determine the diffusion capacitance at 0 V and 0.25 V.
Describe in your own words how diffusion and transition capacitances differ.
Determine the reactance offered by a diode described by the characteristics of Fig. 1.33 at a forward potential of 0.2 V and a reverse potential of -20 V if the applied frequency is 6 MHz.
Sketch the waveform for / of the network of Fig. 1.66 if /, = 2t, and the total reverse recovery time is 9 ns.
Plot lF versus VF using linear scales for the diode of Fig. 1.37, the provided graph employs a log scale for the vertical axis (log scales are covered in Sections 9.2 and 9.3).
Comment on the change in capacitance level with increase in reverse-bias potential for the diode of Fig. 1.37.
Does the reverse saturation current of the diode of Fig. 1.37 change significantly in magnitude for reverse-bias potentials in the range -25 V to -100 V?
For the diode of Fig. 1.37 determine the level of IR at room temperature (25°C) and the boiling point of water (100°C). Is the change significant? Does the level just about double for every 10°C
For the diode of Fig. 1.37, determine the maximum ac (dynamic) resistance at a forward current of 0.1, 1.5, and 20 mA. Compare levels and comment on whether the results support conclusions derived in
Using the characteristics of Fig. 1.37, determine the maximum power dissipation levels for the diode at room temperature (25°C) and 100°C. Assuming that VF remains fixed at 0.7 V, how has the
Using the characteristics of Fig. 1.37, determine the temperature at which the diode current will be 50% of its value at room temperature (25°C).
The following characteristics are specified for a particular Zener diode: Vz = 29 V, VR = 16.8 V, IZT = 10 mA, IR = 20u.A, and IZM 40 mA. Sketch the characteristic curve in the manner displayed in

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