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electrical engineering

Questions and Answers of Electrical Engineering

Given two waves characterized by does y1 (t) = 3 cos wt, y2 (t) = 3 sin (wt +36o) does y2 (t) lead or lag y1 (t), and by what phase angle?
The voltage of an electromagnetic wave traveling on a transmission line is given by v (z, t) =5e-az sin (4π x 109t - 20π2) (V), where z is the distance in meters from the generator. (a)
A certain electromagnetic wave traveling in sea water was observed to have an amplitude of 98.02 (V/m) at a depth of 10 m and an amplitude of 81.87 (V/m) at a depth of 100 m. What is the attenuation
Evaluate each of the following complex numbers and express the result in rectangular form: (a) z1 – 4ejπ/3 (b) z2 – √3 e j3π/4 (c) z3 – 6e– jπ/2 (d) z4 – j3, (e)
Complex numbers z1 and z2 are given byz1 = 3 – j2,z2 = - 4 + J3.(a) Express z1 and z2 in polar form.(b) Find z1 by applying Eq. (1.41) and again by applying Eq. (1.43).(c) Determine the product
If z = 2 + J4, determine the following quantities in polar form:1/z,z3,|z|2Jm {z},Jm {z4}.(Note: In the following solutions, numbers are expressed to only two decimal places, but the final answers
Find complex numbers t = z1 + z2 and s = z1 - z2, both in polar form, for each of the following pairs: (a) z2 – 2 + j3, z2 – 1 – j3, (b) z1 – 3, z2 - - j3, (c) z1 0- 3∟30, z2 – 3
Complex numbers z1 and z2 are given by(a) Determine the product z1z2 in polar form(b) Determine the product z1z2 in polar form(c) Determine the ratio z1z2 in polar form(d) Determine the ratio z1z2 in
If z = 3 – j5, find the value of in (z).
If z = 3 – j4, fine the value of ez.
A voltage source given by vs (t) = 25 cos (2π x 103t – 30o) (V) is connected to a series RC load as shown in Fig. 1-19. If R = 1 MΩ and c = 200 pF, obtain an expression for vc (t), the
Find the phasors of the following time functions: (a) v (t) – 3 cos (wt – π/3) (V), (b) v (t) – 12 sin (wt + π/4) (V), (c) i (x. t)2e–3x sin (wt + π/6) (A), (d) i(t) – 2
Find the instantaneous time sinusoidal functions corresponding to the following phasors: (a) V – 5ejπ/3 (V), (b) V – j6e jπ/4(V), (c) I – (6 + j8) (A), (d) I – – 3 + j2
A series RLC circuit is connected to a generator with a voltage vs (t) = Vo cos (wt + π/3) (V).(a) Write down the voltage loop equation in terms of the current i (t), R, L, C, and vs (t).(b)
A wave traveling along a string is given by y(x, t) = 2 sin (4πt + 10πx) (cm) where x is the distance along the string in meters and y is the vertical displacement. Determine: (a) Te
A laser beam traveling through fog was observed to have an intensity of 1 (μW/m2) at a distance of 2 m from the laser gun and an intensity of 0.2 (μW/m2) at a distance of 3 m. Given that
Complex numbers z1 and z2 are given byZ1 = - 3 +j2Z2 = 1 - j2Determine (a) z1 z2, (b) z1/z*2, (c) z2/1, and (d) z1 z*1, all in polar form
If z = 3ejπ/6, find the value of ez
The voltage source of the circuit shown in the figure is given by vs (t, - 25cos (4, 104t-45o, (v). Obtain an expression for the current flowing through the inductor.
A transmission line of length l connects a load to a sinusoidal voltage source with an oscillation frequency f. assuming the velocity of wave propagation on the line is c, for which of the following
Calculate the line parameters R`, L` G`, and C` for a coaxial line with an inner conductor diameter of 0.5 cm and an outer conductor diameter of 1 cm, filled with an insulating material where μ
A 1-GHz parallel-plate transmission line consists of 1.2-cm-wide copper strips separated by a 0.15-cm-thick layer of polystyrene. Appendix B gives μc = μ0 = 4π x 10-7 (H/m) and σc
Show that the transmission line model shown in Fig. 2-37 (P2.4) yields the same telegrapher’s equations given by Eqs. (2.14) and (2.16)
Find a, B, up, and Zo for the coaxial line of Problem 2.2
Find α, β, up, and Z0 for the coaxial line of Problem 2.6
Such a line is called a distortion less line because despite the fact that it is not lossless, it does nonetheless possess the previously mentioned features of the loss line. Show that for a
For a distortion less line with Z0 – 50 Ω, a – 20 (mNp/m), up – 2.5 x 108 (m/s), find the line parameters and λ at 100 MHz.
Find a and Z0 of a distortion less line whose Rٰ= 2 Ω/m and G` - 2 x 10-4 S/m
A transmission line operating at 125 MHz has Z0 - 40Ω, a – 0.02 (Np/m), and B – 0.75 rad/m. Find the line parameters R`, L`, G`, and C`.
Using a slotted line, the voltage on a lossless transmission line was found to have a maximum magnitude of 1.5 V and a minimum magnitude of 0.6 V. Find the magnitude of the load’s reflection
Polyethylene with εr – 2.25 is used as the insulating material in a lossless coaxial line with characteristic impedance of 50Ω. The radius of the inner conductor is 1.2 mm. (a) What is
50-W lossless transmission line is terminated in a load with Impedance ZL= (30_j50) Ω the wavelength is 8 cm. Find (a) The reflection coefficient at the load, (b) The standing-wave ratio on
On a 150-Ω lossless transmission line, the following observations were noted: distance of first voltage minimum from the load – 3cm; distance of first voltage maximum from the load – 9 cm;
Using a slotted line, the following results were obtained: distance of First minimum from the load = 4 cm; distance of second minimum from the load = 14 cm, voltage standing-wave ratio = 1.5-if the
A load with impedance ZL = (25 = J50) Ω is to be connected to a Lossless transmission line with characteristic impedance Z0, with Z0 chosen such that the standing-wave ratio is the smallest
A 50-W lossless line terminated in a purely resistive load has a Voltage standing wave ratio of 3. Find all possible values of ZL.
At an operating frequency of 300 MHz, a lossless 50-W air-spaced Transmission line 2.5 m in length is terminated with an impedance ZL = (40 + J20) Ω Find the input impedance.
A lossless transmission line of electrical length l = 0.35λ is Terminated in a load impedance as shown in fig. 2-38 (P2-18) find Γ, S, and Zin
Show that the input impedance of a quarter-wavelength long lossless Line terminated in a short circuit appears as an open circuit.
Show that at the position where the magnitude of the voltage on the Line is a maximum the input impedance is purely real.
Find the Laplacian of the following scalar functions: (a) V1 = 10r3 sin2 (b) V2 = (2/R2) cos sin
A cube 2 m on a side is located in the first octant in a Cartesian coordinate system, with one of its corners at the origin. Find the total charge contained in the cube if the charge density is given
Two half-wave dipole antennas, each with impedance of 75, are connected in parallel through a pair of transmission lines, and the combination is connected to a feed transmission line, as shown in
At an operating frequency of 300 MHz, it is desired to use a section of a lossless 50-transmission line terminated in a short circuit to construct an equivalent load with reactance X
A lossless transmission line is terminated in a short circuit. How long (in wavelengths) should the line be in order for it to appear as an open circuit at its input terminals?
The input impedance of a 31-cm-long lossless transmission line of unknown characteristic impedance was measured at 1 MHz. With the line terminated in a short circuit, the measurement yielded an input
A 75-resistive load is preceded by a  4 section of a 50-lossless line, which itself is preceded by another _4 section of a 100-line. What is the input impedance?
A 100-MHz FM broadcast station uses a 300-transmission line between the transmitter and a tower-mounted half-wave dipole antenna. The antenna impedance is 73. You are asked to design a
A 50-MHz generator with Zg = 50 is connected to a load ZL= 50 j25- . The time-average power transferred from the generator into the load is maximum when Zg = Z_L_ where Z _L is the complex
A 50-lossless line of length l = 0 375connects a 300-MHz generator with Vg = 300 V and Zg = 50 to a load ZL. Determine the time-domain current through the load for: (a) ZL =
A generator with Vg = 300 V and Zg = 50 is connected to a load ZL = 75 through a 50-lossless line of length l = 0 15. (a) Compute Zin, the input impedance of the line at the
If the two-antenna configuration shown in Fig. 2-41 (P2.32) is connected to a generator with Vg =250 V and Zg = 50 , how much average power is delivered to each antenna?
For the circuit shown in Fig. 2-42 (P2.33), calculate the average incident power, the average reflected power, and the average power transmitted into the infinite 100-line. The
An antenna with a load impedance ZL = (75 + j25) is connected to a transmitter through a 50-lossless transmission line. If under matched conditions (50-load), the transmitter
Use the Smith chart to find the reflection coefficient corresponding to a load impedance:(a) ZL = 3Z0,(b) ZL = (2 - 2 j) Z0,(c) ZL = 2 jZ0,(d) ZL = 0 (short circuit).
Use the Smith chart to find the normalized load impedance corresponding to a reflection coefficient: (a) 0. 5, (b) 0. 5 60o, (c)
On a lossless transmission line terminated in a load ZL = 100 , the standing-wave ratio was measured to be 2.5. Use the Smith chart to find the two possible values of Z0.
A lossless 50-transmission line is terminated in a load with ZL = (50 + j25) . Use the Smith chart to find the following:(a) The reflection coefficient,(b) The standing-wave ratio,(c) The
A lossless 50-transmission line is terminated in a short circuit. Use the Smith chart to find (a) The input impedance at a distance 2.3from the load, (b) The
Use the Smith chart to find yL if zL = 1.5 - j0. 7
A lossless 100-transmission line 38 in length is terminated in an unknown impedance. If the input impedance is Zin = j2.5 , (a) Use the Smith chart to find
A 75-W lossless line is 0.6 long. If S = 1.8 and θr = - 60o, use the Smith chart to find ZL and Zin
Using a slotted line on a 50-W air-spaced lossless line, the following measurements were obtained: S =1.6, [V] max occurred only at 10 cm and 24 cm from the load. Use the Smith chart to find ZL
At an operating frequency of 5 GHz, a 50-lossless coaxial line with insulating material having a relative permittivity r = 2.25 is terminated in an antenna with an impedance ZL = 150 Use the
A 50-loss-less line 0.6long is terminated in a load with ZL = (50 + j25) W. At 0.3from the load, a resistor with resistance R =30 is connected as shown in Fig. 2-43 (P2.45 (a). Use
A 50-lossless line is to be matched to an antenna with ZL = (75 - j20) using a shorted stub. Use the Smith chart to determine the stub length and the distance between the antenna and
Repeat Problem 2.46 for a load with ZL = (100, j50).
Use the Smith chart to find Zin of the feed line shown in Fig. 2-44 (P2.48 (a)). All lines are lossless with Z0 = 50 .
Repeat Problem 2.48 for the case where all three transmission lines are 4 in length
Generate a bounce diagram for the voltage V (z, t) for a 1-m long lossless line characterized by Z0 = 50  and up = 2c/3 (where c is the velocity of light) if the line is fed by a step voltage
Repeat Problem 2.50 for the current I on the line.
In response to a step voltage, the voltage waveform shown in Fig. 2-45 (P2.52) was observed at the sending end of a lossless transmission line with Rg = 50 , Z0 = 50 , and r =
In response to a step voltage, the voltage waveform shown in Fig. 2.46 (P2.53) was observed at the sending end of a shorted line with Z0 = 50 and r = 4. Determine Vg, Rg, and
Suppose the voltage waveform shown in Fig. 2-45 was observed at the sending end of a 50-transmission line in response to a step voltage introduced by a generator with Vg = 15 V and an
A generator circuit with Vg = 200 V and Rg = 25 was used to excite a 75-lossless line with a rectangular pulse of duration 0.4 μs. The line is 200 m long, its up = 2 x 108 m/s, and it is
For the circuit of Problem 2.55, generate a bounce diagram for the current and plot its time history at the middle of the line.
For the parallel-plate transmission line of Problem 2.3, the line parameters are given by:Find , , up, and Z0 at 1 GHz
A 300-lossless air transmission line is connected to a complex load composed of a resistor in series with an inductor, as shown in the figure. At 5 MHz, determine: (a) , (b) S, (c)
A 50-lossless transmission line is connected to a load composed of a 75-resistor in series with a capacitor of unknown capacitance. If at 10 MHz the voltage standing wave ratio on the line
A 50-lossless line is terminated in a load impedance ZL = (30 - j20).(a) Calculate and S.(b) It has been proposed that by placing an appropriately selected resistor across the
For the lossless transmission line circuit shown in the figure, determine the equivalent series lumped-element circuit at 400 MHz at the input to the line. The line has a characteristic impedance of
The circuit shown in the figure consists of a 100-lossless transmission line terminated in a load with ZL = (50 + j100) . If the peak value of the load voltage was measured to be |V L| =12 V,
Use the Smith chart to determine the input impedance Zin of the two-line configuration shown in the figure.
A 25-antenna is connected to a 75-lossless transmission line. Reflections back toward the generator can be eliminated by placing a shunt impedance Z at a distance l from the load.
In response to a step voltage, the voltage waveform shown in the figure below was observed at the midpoint of a lossless transmission line with Z0 = 50 and up = 2 X 108 m/s.
Vector A starts at point (1, - 1, - 3) and ends at point (2, - 1, 0). Find a unit vector in the direction of A.
Given vectors A = x2 y3 z, B = x2 y z3, and C = x4 y2 z2, show that C is perpendicular to both A and B.
In Cartesian coordinates, the three corners of a triangle are P1 (0, 4, 4). P2 (4, - 4, 4), and P3 (2, 2, - 4) find the area of the triangle.
Given A = x2 _ y3 + z1 and B = xBx + y2 + zBz:(a) Find Bx and Bz if A is parallel to B;(b) Find a relation between Bx and Bz if A is perpendicular to B.
Given vectors A = x + y2 _ z3, B = x2 _ y4, and C = y2 _z4, find (a) A and a, (b) The component of B along C, (c) AC, (d) A x C, (e) A. (B ^ C), (f) A x (B x C), (g) x x B, and (h)
Given vectors A = x2 – y + z3 and B = x3 – z2, find a vector C whose magnitude is 9 and whose direction is perpendicular to both A and B.
Given A = x(x 2y) y(y 3z z(3x y), determine a unit vector parallel to A at point P(1, - 1, 2)
By expansion in Cartesian coordinates, prove:(a) The relation for the scalar triple product given by (3.29), and(b) The relation for the vector triple product given by (3.33).
Find an expression for the unit vector directed toward the origin from an arbitrary point on the line described by x = 1 and z = 2.
Find an expression for the unit vector directed toward the point P located on the z-axis at a height h above the x–y plane from an arbitrary point Q(x, y, - 3) in the plane z = - 3.
Find a unit vector parallel to either direction of the line described by 2x z – 4.
Two lines in the x–y plane are described by the expressions:Line 1 x + 2y = -6Line 2 3x + 4y = 8Use vector algebra find the smaller angle between type lines at their intersection =point.
A given line is described by x + 2y = 4. Vector A starts at the origin and ends at point P on the line such that A is orthogonal to the line. Find and expression for A
Show that, given two vectors A and B,(a) The vector C defined as the vector component of B in the direction of A is given byWhere a is the unit vector of A, and(b) The vector D defined as the vector
A certain plane is described by 2x + 3y + 4z = 16 Find the unit vector normal to the surface in the dir section away from the origin.

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