The batteries shown in the circuit in Fig. E26.24 have negligibly small internal resistances. Find the current through (a) The 30.0- resistor; (b) The 20.0- resistor; (c) The 10.0-V Figure E26.24...
A heart defibrillator is used to enable the heart to start beating if it has stopped. This is done by passing a large current of 12 A through the body at 25 V for a very short time, usually about 3.0...
Scientists are working on a new technique to kill cancer cells by zapping them with ultrahigh-energy (in the range of 10 12 W) pulses of light that last for an extremely short time (a few...
The vitreous humor, a transparent, gelatinous fluid that fills most of the eyeball, has an index of refraction of 1.34. Visible light ranges in wavelength from 380 nm (violet) to 750 nm (red), as...
Very short pulses of high-intensity laser beams are used to repair detached portions of the retina of the eye. The brief pulses of energy absorbed by the retina weld the detached portions back into...
A flat piece of glass covers the top of a vertical cylinder that is completely filled with water. If a ray of light traveling in the glass is incident on the interface with the water at an angle of ...
Light of original intensity l 0 passes through two ideal polarizing filters having their polarizing axes oriented as shown in Fig. E33.32. You want to adjust the angle Ï so that the intensity at...
A long, straight solenoid has 800 turns. When the current in the solenoid is 2.90 A, the average flux through each turn of the solenoid is 3.25 10 -3 Wb. What must be the magnitude of the rate of...
Two insulated wires perpendicular to each other in the same plane carry currents as shown in Fig. E28.29. Find the magnitude of the net magnetic field these wires produce at points P and Q if the...
A parallel-plate capacitor is made from two plates 12.0 cm on each side and 4.50 mm apart. Half of the space between these plates contains only air, but the other half is filled with Plexiglas ®...
A uniform line charge of 16 nC/m is located along the line defined by y = 2, z = 5. If = 0: (a) Find E at P(1, 2, 3). (b) Find E at that point in the z = 0 plane where the direction of E is given by...
Given the surface charge density, s = 2C/m 2 , existing in the region < 0.2 m, z = 0, find E at (a) P A ( = 0, z = 0.5); (b) P B ( = 0, z = 0.5). Show that (c) The field along the z axis reduces...
Surface charge of uniform density Ï s lies on a spherical shell of radius b, centered at the origin in free space. (a) Find the absolute potential everywhere, with zero reference at infinity....
A spherically symmetric charge distribution in free space (with 0 < r < ) is known to have a potential function V(r ) = V 0 a 2 /r 2 , where V 0 and a are constants. (a) Find the electric field...
(a) Using data tabulated in Appendix C, calculate the required diameter for a 2-m-long nichrome wire that will dissipate an average power of 450 W when 120 V rms at 60 Hz is applied to it. (b)...
Let the cylindrical surfaces = 4 cm and = 9 cmenclose two wedges of perfect dielectrics, r1 = 2 for 0 < < /2 and r2 = 5 for /2 < < 2. If E1 = (2000/)a V/m, find (a) E 2 ; (b) The total...
Using the uniqueness property of the Fourier series, find exponential Fourier series for the following signals (f 0 is an arbitrary frequency): (a) x 1 (t) = sin 2 (2f 0 t) (b) x 2 (t) = cos(2f 0 t)...
An AM modulator operates with the message signal m(t) = 9 cos (20t) - 8 cos (60t) The unmodulated carrier is given by 110 cos(200t) and the system operates with an index of 0.8. (a) Write the...
A sinusoidal message signal has a frequency of 250 Hz. This signal is the input to an FM modulator with an index of 8. Determine the bandwidth of the modulator output if a power ratio, P r , of 0.8...
In a certain digital data transmission system the probability of a bit error as a function of timing jitter is given by where z is the signal-to-noise ratio, |ÎT|, is the timing jitter, and T...
A simple model for a multi path communications channel is shown in Figure 5.20(a). Figure 5.20 (a) (a) Find H c (f) = Y(f) / X (f) for this channel and plot |H c (f)| for β = 1 and 0.5....
Using only the Fourier transform of the unit impulse function and the differentiation theorem, find the Fourier transforms of the signals shown in Figure 2.36.
The random variable has pdf where u(x) is the unit step. Determine the mean and the variance of the random variable thus defined. fx(x) = ;5(x 5) + lu(x 4) u(x 8)]
A circle is divided into 21 equal parts. A pointer is spun until it stops on one of the parts, which are numbered from 1 through 21. Describe the sample space and, assuming equally likely outcomes,...
Two random variables X and Y have means and variances given below: m x = 1 2 x = 4 m y = 3 2 y = 7 A new random variable Z is defined as Z = 3X - 4Y Determine the mean and variance of Z for each of...
Referring to Problem 7.1, what are the following probabilities for each case? (a)F X (X ¤ 2A,t = 4) (b)F X (X ¤ 0,t = 4) (c)F X (X ¤ 2A,t = 2) Data From Problem 7.1 A fair die is...
The surface x = 0 separates two perfect dielectrics. For x > 0, let r = r 1 = 3, while r 2 = 5 where x < 0. If E 1 = 80a x 60a y 30a z V/m, find (a) EN 1 ; (b) ET 1 ; (c) E 1 ; (d) The angle 1...
A load, Z L = 25+ j75 , is located at z = 0 on a lossless two-wire line for which Z 0 = 50 and v = c. (a) If f = 300 MHz, find the shortest distance d (z = d) at which the input admittance has a...
With the aid of the Smith chart, plot a curve of |Z in | versus l for the transmission line shown in Figure 10.33. Cover the range 0 < l/λ < 0.25. 20 Lossless Lossless 20 Zo = 50 2 Zo...
Given two independent, wide-sense stationary random processes X(t) and Y(t) with auto correlation functions R x () and R Y (), respectively. (a) Show that the auto correlation function R Z () of...
The normalized load on a lossless transmission line is 2 + j 1. Let = 20 m and make use of the Smith chart to find (a) The shortest distance from the load to a point at which z in = r in + j0, where...
A lossless transmission line having characteristic impedance Z 0 = 50 is driven by a source at the input end that consists of the series combination of a 10-V sinusoidal generator and a 50-resistor....
The parallel-plate transmission line shown in Figure 9.7 has dimensions b = 4 cm and d = 8 mm, while the medium between the plates is characterized by μ r = 1, r = 20, and Ï = 0....
Consider the region defined by |x|, |y|, and |z| < 1. Let r = 5, r = 4, and = 0. If J d = 20 cos(1.5 10 8 t bx)a y A/m 2 (a) Find D and E; (b) Use the point form of Faradays law and an...
The cones θ = 21¦ and θ = 159¦ are conducting surfaces and carry total currents of 40 A, as shown in Figure 8.17. The currents return on a spherical conducting...
A small bead slides around a horizontal circle at height y inside the cone shown in FIGURE CP8.69. Find an expression for the beads speed in terms of a, h, y, and g. a FIGURE CP8.69
A student has 65-cm-long arms. What is the minimum angular velocity (in rpm) for swinging a bucket of water in a vertical circle without spilling any? The distance from the handle to the bottom of...
A 500 g model rocket is on a cart that is rolling to the right at a speed of 3.0 m/s. The rocket engine, when it is fired, exerts an 8.0 N vertical thrust on the rocket. Your goal is to have the...
A hollow tubular conductor is constructed from a type of brass having a conductivity of 1.2 10 7 S/m. The inner and outer radii are 9 and 10 mm, respectively. Calculate the resistance per meter...
A uniform plane wave in free space has electric field vector given by E s = 10e jx a z + 15e jx a y V/m. (a) Describe the wave polarization. (b) Find H s . (c) Determine the average power density in...
A right-circularly polarized plane wave is normally incident from air onto a semi-infinite slab of plexiglas (' r = 3.45, " r = 0). Calculate the fractions of the incident power that are reflected...
An air-filled rectangular waveguide is to be constructed for single-mode operation at 15 GHz. Specify the guide dimensions, a and b, such that the design frequency is 10 percent higher than the...
Consider a sphere of radius r = 4 centered at (0, 0, 3). Let S 1 be that portion of the spherical surface that lies above the xy plane. Find S1 ( H) dS if H = 3 a in cylindrical coordinates.
A coaxial cable has conductor dimensions of a = 1.0 mm and b = 2.7 mm. The inner conductor is supported by dielectric spacers ( r = 5) in the form of washers with a hole radius of 1 mm and an outer...
The inner conductor of the transmission line shown in Figure 6.13 has a square cross section 2a ? 2a, whereas the outer square is 4a ? 5a. The axes are displaced as shown. (a) Construct a good-sized...
In free space, let = 2000/r 2.4 . (a) Use Poissons equation to find V(r) if it is assumed that r 2 E r 0 when r 0, and also that V 0 as r . (b) Now find V(r) by using Gausss law and a line...
A current sheet K = 8a x A/m flows in the region 2 < y < 2 in the plane z = 0. Calculate H at P(0, 0, 3).
A rectangular loop of wire in free space joins point A(1, 0, 1) to point B(3, 0, 1) to point C(3, 0, 4) to point D(1, 0, 4) to point A. The wire carries a current of 6 mA, flowing in the a z...
Show that (9.162) is the average energy in terms of Î for binary antipodal ASK. (9.162) Hc(f) = 1, |f| < %3D
Determine the output current in the circuit of Fig. 4.60. Fig. 4.60: Vcc= 15 V 20 k 1 Q1 Q2 10 k
Determine the output voltage as a function of the input voltage for the circuit of Fig. 6.54. Assume the op amp is ideal. Figure 6.54 1 k2 1 Vout +0 Vin
Determine the overall input resistance, voltage gain, and output resistance of the CC-CB connection of Fig. 3.79. Neglect r o , r μ , and r b . Note that the addition of a...
Derive and sketch the complete small-signal equivalent circuit for the device of Problem 1.15 with V GS = 1 V, V DS = 2 V, and V SB = 1 V. Use 0 = 0.7 V, C sb0 = C db0 = 20 fF, and C gb = 5 fF....
Use the device data of Problems 1.15 and 1.16 to calculate the frequency of unity current gain of this transistor with V DS = 3V, V SB = 0 V, V GS = 1 V, 1.5 V, and 2 V. Data from Prob. 1.16: Derive...
Draw the block diagram of an M -power law circuit for synchronizing a local carrier for 8-PSK. Assume that f c = 10 MHz and T s = 0.1 ms. Care fully label all blocks, and give critical frequencies...
Use half-circuit analysis to determine A dm , A cm , A cmdm , and A dmcm for a resistively loaded differential pair with mismatched resistive loads, R 1 and R 2 . Assume that R 1 = 10.1 k and R 2 =...
Calculate an analytical expression for the small-signal output resistance R o of the bipolar cascode current mirror of Fig. 4.8. Assume that the input current source is not ideal and that the...
Calculate the output resistance of the Wilson current mirror shown in Fig. 4.57. What is the percentage change in I OUT for a 5-V change in VOUT? Compare your answer with a SPICE simulation using a...
Assume that you have a standard deck of 52 cards (jokers have been removed). (a) What is the information associated with the drawing of a single card from the deck? (b) What is the information...
Calculate the small-signal voltage gain of the common-source amplifier with active load in Fig. 4.16b.Assume that V DD = 3 V and that all the transistors operate in the active region. Do the...
Calculate the small-signal voltage gain of a common-source amplifier with depletion load in Fig. 4.20, including both the body effect and channel-length modulation. Assume that V DD = 3 V and that...
Using (8.146), derive an expression for the ratio of the noise power in y D (t) with de-emphasis to the noise power in y D (t) without de-emphasis. Plot this ratio as a function of W/f 3 . Evaluate...
One of the most amusing things a person can experience is that in certain parts of the world a still car on neutral going uphill when its brakes are released. Such occurrences are even broadcast on...
For the circuit of Fig. 5.10, assume that V CC = 12 V, R L = 1 kΩ, and V CE(sat) = 0.2 V. Assume that there is sufficient sinusoidal input voltage available at V i to drive V o to its...
For the circuit of Problem 5.10, calculate and sketch the waveforms of I c1 , V ce1 , and P c1 for device Q 1 over one cycle. Do this for output voltage amplitudes (zero to peak) of 11.5 V, 6 V, and...
At 45 latitude, the gravitational acceleration as a function of elevation z above sea level is given by g = a - bz, where a = 9.807 m/s 2 and b = 3.32 10 -6 s -2 . Determine the height above sea...
A 3kg rock is thrown upward with a force of 200 N at a location where the local gravitational acceleration is 9.79 m/s 2 . Determine the acceleration of the rock, in m/s 2 .
For the circuit of Fig. 5.25, assume that V CC = 15V, F (pnp) = 30, F (npn) = 150, I S (npn) = 10 14 A, I S (pnp) = 10 15 A, and for all devices V BE(on) = 0.7 V, V CE(sat) = 0.2 V. Assume that Q 5...
Somebody proposes the following system to cool a house in the summer: Compress the regular outdoor air, let it cool back to the outdoor temperature, pass it through a turbine, and discharge the cold...
Air enters a nozzle steadily at 280 kPa and 77C with a velocity of 50 m/s and exits at 85 kPa and 320 m/s. The heat losses from the nozzle to the surrounding medium at 20C are estimated to be 3.2...
A 1.2-mm-diameter tube is inserted into an unknown liquid whose density is 960 kg/m 3 , and it is observed that the liquid rises 5 mm in the tube, making a contact angle of 15. Determine the surface...
In the circuit of Fig. 6.55, determine the cor-rect value ofRxso that the output voltage is zero when the input voltage is zero. Assume a nonzero input bias current, but zero input offset current and...
Blocks a, b, and c in FIGURE Q14.7 have the same density. Rank in order, from largest to smallest, the sizes of the buoyant forces F a , F b , and F c on a, b, and c. Explain. 50 g 40 g 50 g
Gas flows through the pipe of FIGURE Q14.10. You cant see into the pipe to know how the inner diameter changes. Rank in order, from largest to smallest, the gas speeds v a , v b , and v c at points...
The container shown in FIGURE EX14.12 is filled with oil. It is open to the atmosphere on the left. a. What is the pressure at point A? b. What is the pressure difference between points A and B?...
How far must a 2.0-cm-diameter piston be pushed down into one cylinder of a hydraulic lift to raise an 8.0-cm-diameter piston by 20 cm?
Calculate the low-frequency PSRR from the Vdd andVss power supplies for the common-source amplifier shown in Fig. 6.57. Assume the transistor is biased in the active region. Figure 6.57 VDD + Vdd ER...
The bottom of a steel boat is a 5.0 m 10 m 2.0 cm piece of steel ( steel = 7900 kg/m 3 ). The sides are made of 0.50-cm thick steel. What minimum height must the sides have for this boat to float...
Air flows through the tube shown in FIGURE P14.67. Assume that air is an ideal fluid. a. What are the air speeds v 1 and v 2 at points 1 and 2? b. What is the volume flow rate? 2.0 mm 2. 1.0 cm Air...
Air flows through the tube shown in FIGURE P14.66 at a rate of 1200 cm 3 /s. Assume that air is an ideal fluid. What is the height h of mercury in the right side of the U-tube? 4.0 mm 2.0 cm 1200...
A hurricane wind blows across a 6.0 m 15.0 m flat roof at a speed of 130 km/h. a. Is the air pressure above the roof higher or lower than the pressure inside the house? Explain. b. What is the...
The weight of a body is usually measured by disregarding buoyancy force applied by the air. Consider a 20-cm-diameter spherical body of density 7800 kg/m 3 . What is the percentage error associated...
The 0.5-m-radius semi-circular gate shown in the figure is hinged through the top edge AB. Find the required force to be applied at the center of gravity to keep the gate closed. = 80 kPa (abs) alr...
A 30-ton, 4-m-diameter hemispherical dome on a level surface is filled with water, as shown in Fig. P11??48. Someone claims that he can lift this dome by making use of Pascal??s law by attaching a...
A glass manometer with oil as the working fluid is connected to an air duct as shown in Fig. P12??11. Will the oil levels in the manometer be as in Fig. P12??11Ca or b? Explain. What would your...
A piezometer and a Pitot tube are tapped into a 4-cm-diameter horizontal water pipe, and the height of the water columns are measured to be 26 cm in the piezometer and 35 cm in the Pitot tube (both...
Given the spherically symmetric potential field in free space, V = V 0 e r/a , find. (a) at r = a; (b) The electric field at r = a; (c) The total charge.
A small object moves along the x-axis with acceleration a x (t) = -(0.0320 m/s 3 )(15.0 s - t). At t = 0 the object is at x = -14.0 m and has velocity v 0x = 8.00 m/s. What is the x-coordinate of the...
For the amplifier in Problem 9.1, calculate and sketch plots of gain (in decibels) and phase versus frequency (log scale) with no feedback applied. Determine the value of f that just causes...
An op amp has a low-frequency open-loop voltage gain of 100,000 and a frequency response with a single negative-real pole with magnitude 5 Hz. This amplifier is to be connected in a series-shunt...
A woman stands in the middle of a perfectly smooth, frictionless, frozen lake. She can set herself in motion by throwing things, but suppose she has nothing to throw. Can she propel herself to shore...
An egg is released from rest from the roof of a building and falls to the ground. Its fall is observed by a student on the roof of the building, who uses coordinates with origin at the roof, and by a...
The ac schematic of an amplifier is shown in Fig. 11.49. The circuit is fed from a current source i S and data are as follows: R S =1 k ¦ R L = 10 k ¦ I C = 1 mA β = 50 r b...
The CMOS circuit of Fig. 9.56 is to be used as a high-slew-rate op amp. A load capacitance of C L = 10 pF is connected from V o to ground. Supply voltages are ± 5 V and I 1 = 20 µA....
You swing a ball on the end of a lightweight string in a horizontal circle at constant speed. Can the string ever be truly horizontal? If not, would it slope above the horizontal or below the...
An analog source has an output described by the probability density function The output of the source is quantized into 10 messages using the eleven quantizing levels x i = 0.1k, k = 0,1,.....,10 The...
Find z = E b / N 0 required to give P E = 10 -5 for the following coherent digital modulation techniques: (a) binary ASK; (b) BPSK; (c) binary FSK; (d) BPSK with no carrier component but with a phase...
Given the three signals (a) Sketch each one and show that each has energy of A 2 T. (b) Show that R 12 , = 0 for each of the combinations (A, B), (B, C), and (A, C). What is the optimum threshold for...
As an approximation to the integrate-and-dump detector in Figure 9.3(a), we replace the integrator with a low pass RC filter with frequency response function where f 3 is the 3-dB cut off frequency...
When a tall, heavy refrigerator is pushed across a rough floor, what factors determine whether it slides or tips?