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Principles and Applications of Electrical Engineering

Giorgio Rizzoni

Chapter 15

Electronic Instrumentation and Measurements - all with Video Answers

Educators

Chapter Questions

Problem 1

Most motorcycles have engine speed tachometers,
as well as speedometers, as part of their
instrumentation. What differences, if any, are there
between the two in terms of transducers?

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01:13

Problem 2

Explain the differences between the engineering
specifications you would write for a transducer to
measure the frequency of an audible sound wave and a
transducer to measure the frequency of a visible light
wave.

Shital Rijal
Shital Rijal
Numerade Educator
00:34

Problem 3

.A measurement of interest in the summer is the
temperature-humidity index, consisting of the sum of
the temperature and the percentage relative humidity.
How would you measure this? Sketch a simple
schematic diagram.

Subhadeepta Sahoo
Subhadeepta Sahoo
Numerade Educator
01:23

Problem 4

Consider a capacitive displacement transducer as shown in Figure P15.4. Its capacitance is determined by the equation

$$
C=\frac{0.255 A}{d} \mathrm{~F}
$$
where $A=$ cross-sectional area of the transducer plate (in ${ }^2$ ), and $d=$ air-gap length (in). Determine the change in voltage ( $\Delta v_0$ ) when the air gap changes from 0.01 in to 0.015 in .

Narayan Hari
Narayan Hari
Numerade Educator

Problem 5

The circuit of Figure P15.5 may be used for operation of a photodiode. The voltage $V_D$ is a reverse-bias voltage large enough to make diode current, $i_D$, proportional to the incident light intensity, $H$. Under this condition, $i_D / H=0.5 \mu \mathrm{~A}-\mathrm{m}^2 / \mathrm{W}$.
a. Show that the output voltage, $V_{\text {out }}$, varies linearly with $H$.
b. If $H=1,500 \mathrm{~W} / \mathrm{m}^2, V_D=7.5 \mathrm{~V}$, and an output voltage of 1 V is desired, determine an appropriate value for $R_L$.

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02:43

Problem 6

G is a material constant equal to $0.055 \mathrm{~V}-\mathrm{m} / \mathrm{N}$ for quartz in compressive stress and $0.22 \mathrm{~V}-\mathrm{m} / \mathrm{N}$ for polyvinylidene fluoride in axial stress.
a. A force sensor uses a piezoelectric quartz crystal as the sensing element. The quartz element is 0.25 in thick and has a rectangular cross section of $0.09 \mathrm{in}^2$. The sensing element is compressed and the output voltage measured across the thickness. What is the output of the sensor in volts per newton?
b. A polyvinylidene fluoride film is used as a piezoelectric load sensor. The film is $30 \mu \mathrm{~m}$ thick, 1.5 cm wide, and 2.5 cm in the axial direction. It is stretched by the load in the axial direction, and the output voltage is measured across the thickness. What is the output of the sensor in volts per newton?

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
07:16

Problem 7

Let $b$ be the damping constant of the mounting structure of a machine as pictured in Figure P15.7. It must be determined experimentally. First, the spring constant, $K$, is determined by measuring the resultant displacement under a static load. The mass, $m$, is directly measured. Finally, the damping ratio, $\xi$, is
measured using an impact test. The damping constant is given by $b=2 \xi \sqrt{\mathrm{Km}}$. If the allowable levels of error in the measurements of $K, m$, and $\xi$ are $\pm 5$ percent, $\pm 2$ percent, and $\pm 10$ percent respectively, estimate a percentage error limit for $b$.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
01:46

Problem 8

The quality control system in a plant that makes acoustical ceiling tile uses a proximity sensor to measure the thickness of the wet pulp layer every 2 feet along the sheet, and the roller speed is adjusted based on the last 20 measurements. Briefly, the speed is adjusted unless the probability that the mean thickness lies within $\pm 2 \%$ of the sample mean exceeds 0.99 .
A typical set of measurements (in mm ) is as follows:
$8.2,9.8,9.92,10.1,9.98,10.2,10.2,10.16,10.0,9.94$,
$9.9,9.8,10.1,10.0,10.2,10.3,9.94,10.14,10.22,9.8$
Would the speed of the rollers be adjusted based on these measurements?

Victor Salazar
Victor Salazar
Numerade Educator
02:33

Problem 9

Discuss and contrast the following terms:
a. Measurement accuracy.
b. Instrument accuracy.
c. Measurement error.
d. Precision.

Mahendra Kumar
Mahendra Kumar
Numerade Educator
06:15

Problem 10

Four sets of measurements were taken on the same response variable of a process using four different sensors. The true value of the response was known to be constant. The four sets of data are shown in Figure P15.10. Rank these data sets (and hence the sensors) with respect to:
a. Precision.
b. Accuracy.

Nicole Powell
Nicole Powell
Numerade Educator

Problem 11

For the instrumentation amplifier of Figure P15.11, find the gain of the input stage if $R_1=1 \mathrm{k} \Omega$ and $R_2=5 \mathrm{k} \Omega$.

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Problem 12

Consider again the instrumentation amplifier of Figure P15.4. Let $R_1=1 \mathrm{k} \Omega$. What value of $R_2$ should be used to make the gain of the input stage equal 50?

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00:50

Problem 13

Again consider the instrumentation amplifier of Figure P15.11. Let $R_2=10 \mathrm{k} \Omega$. What value of $R_1$ will yield an input-stage gain of 16 ?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
00:50

Problem 14

For the IA of Figure 15.16, find the gain of the input stage if $R_1=1 \mathrm{k} \Omega$ and $R_2=10 \mathrm{k} \Omega$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator

Problem 15

For the IA of Figure 15.16, find the gain of the input stage if $R_1=1.5 \mathrm{k} \Omega$ and $R_2=80 \mathrm{k} \Omega$.

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Problem 16

Find the differential gain for the IA of Figure 15.16 if $R_2=5 \mathrm{k} \Omega, R_1=R^{\prime}=R=1 \mathrm{k} \Omega$, and $R_F=10 \mathrm{k} \Omega$.

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02:30

Problem 17

Suppose, for the circuit of Figure P15.11, that $R_F=200 \mathrm{k} \Omega, R=1 \mathrm{k} \Omega$, and $\Delta R=2 \%$ of $R$. Calculate the common-mode rejection ratio (CMRR) of the instrumentation amplifier. Express your result in dB.

Narayan Hari
Narayan Hari
Numerade Educator

Problem 18

Given the instrumentation amplifier of Figure P15.11, with the component values of Problem 15.17, calculate the mismatch in gains for the differential components. Express your result in dB .

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Problem 19

Given $R_F=10 \mathrm{k} \Omega$ and $R_1=2 \mathrm{k} \Omega$ for the IA of Figure 15.16, find $R$ and $R_2$ so that a differential gain of 900 can be achieved.

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Problem 20

Replace the cutoff frequency specification of Example 15.3 with $\omega_C=10 \mathrm{rad} / \mathrm{s}$ and determine the order of the filter required to achieve 40 dB attenuation at $\omega_S=24 \mathrm{rad} / \mathrm{s}$.

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02:27

Problem 21

The circuit of Figure P15.21 represents a low-pass filter with gain.
a. Derive the relationship between output amplitude and input amplitude.
b. Derive the relationship between output phase angle and input phase angle.

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator

Problem 22

Consider again the circuit of Figure P15.21. Let $R_{\text {in }}=20 \mathrm{k} \Omega, R_F=100 \mathrm{k} \Omega$, and $C_F=100 \mathrm{pF}$. Determine an expression for $v_{\text {out }}(t)$ if $v_{\text {in }}(t)=2 \sin$ $(2,000 \pi t) \mathrm{V}$.

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02:16

Problem 23

Derive the frequency response of the low-pass filter of Figure 15.22.

Arpit Gupta
Arpit Gupta
Numerade Educator

Problem 24

Derive the frequency response of the high-pass filter of Figure 15.22.

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04:55

Problem 25

Derive the frequency response of the band-pass filter of Figure 15.22.

Amit Srivastava
Amit Srivastava
Numerade Educator
01:01

Problem 26

Consider again the circuit of Figure P15.21. Let $C_F=100 \mathrm{pF}$. Determine appropriate values for $R_{\text {in }}$ and $R_F$ if it is desired to construct a filter having a cutoff frequency of 20 kHz and a gain magnitude of 5 .

Amit Srivastava
Amit Srivastava
Numerade Educator

Problem 27

Design a second-order Butterworth high-pass filter with a $10-\mathrm{kHz}$ cutoff frequency, a DC gain of 10 , $Q=5$, and $V_S= \pm 15 \mathrm{~V}$.

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Problem 28

Design a second-order Butterworth high-pass filter with a $25-\mathrm{kHz}$ cutoff frequency, a DC gain of 15 , $Q=10$, and $V_S= \pm 15 \mathrm{~V}$.

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Problem 29

The circuit shown in Figure P15.29 is claimed to exhibit a second-order Butterworth low-pass voltage gain characteristic. Derive the characteristic and verify the claim.

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02:07

Problem 30

Design a second-order Butterworth low-pass filter with a $15-\mathrm{kHz}$ cutoff frequency, a DC gain of 15 , $Q=5$, and $V_S= \pm 15 \mathrm{~V}$.

Narayan Hari
Narayan Hari
Numerade Educator

Problem 31

Design a band-pass filter with a low cutoff frequency of 200 Hz , a high cutoff frequency of 1 kHz , and a pass-band gain of 4. Calculate the value of $Q$ for the filter. Also, draw the approximate frequency response of this filter.

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Problem 32

Using the circuit of Figure P15.29, design a second-order low-pass Butterworth filter with a cutoff frequency of 10 Hz .

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Problem 33

A low-pass Sallen-Key filter is shown in Figure P15.33. Find the voltage gain $V_{\text {out }} / V_{\text {in }}$ as a function of frequency and generate its Bode magnitude plot. Show and observe that the cutoff frequency is $1 / 2 \pi R C$ and that the low-frequency gain is $R_4 / R_3$.

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02:27

Problem 34

The circuit shown in Figure P15.34 exhibits low-pass, high-pass, and band-pass voltage gain characteristics, depending on whether the output is taken at node 1, node 2, or node 3. Find the transfer functions relating each of these outputs to $V_{\text {in }}$, and determine which is which.

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator

Problem 35

The filter shown in Figure P15.35 is called an infinite-gain multiple-feedback filter. Derive the following expression for the filter's frequency response:

$$
\begin{aligned}
& H(j \omega)=-\left(1 / R_3 R_2 C_1 C_2\right) R_3 / R_1 \\
& (j \omega)^2+\left(\frac{1}{R_1 C_1}+\frac{1}{R_2 C_1}+\frac{1}{R_3 C_1}\right) j \omega+\frac{1}{R_3 R_2 C_1 C_2}
\end{aligned}
$$

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Problem 36

The filter shown in Figure P15.36 is a Sallen and Key band-pass filter circuit, where $K$ is the DC gain of the filter. Derive the following expression for the filter's frequency response:

$$
\begin{aligned}
& H(j \omega)= \\
& (j \omega)^2+j \omega\left(\frac{1}{R_1 C_1}+\frac{1}{R_3 C_2}+\frac{1}{R_3 C_1}+\frac{1-K}{R_2 C_1}\right)+\frac{R_1+R_2}{R_1 R_2 R_3 C_1 C_2}
\end{aligned}
$$

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Problem 37

Show that the expression for $Q$ in the filter of Problem 15.35 is given by

$$
\frac{1}{Q}=\sqrt{R_2 R_3 \frac{C_2}{C_1}}\left(\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}\right)
$$

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Problem 38

List two advantages of digital signal processing over analog signal processing.

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Problem 39

Discuss the role of a multiplexer in a data acquisition system.

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Problem 40

The circuit shown in Figure P15.40 represents a sample-and-hold circuit, such as might be used in a successive-approximation ADC. Assume that the JFET is turned on when $V_G$ is high, and off when $V_G$ is low. Explain the operation of the circuit.

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Problem 41

For the circuit shown in Figure P15.40, let $V_{\text {in }}$ be a 1 kHz sinusoidal signal with $0^{\circ}$ phase angle, 0 V DC offset, and 20 V peak-to-peak amplitude. Let $V_G$ be a rectangular pulse train, with pulse width $10 \mu \mathrm{~s}$, and
period $100 \mu \mathrm{~s}$, with the leading edge of the first pulse at $t=0$.
a. Sketch $V_{\text {out }}$ if the $R C$ circuit has a time constant equal to $20 \mu \mathrm{~s}$.
b. Sketch $V_{\text {out }}$ if the $R C$ circuit has a time constant equal to 1 ms .

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Problem 42

The unsigned decimal number $12_{10}$ is inputted to a four-bit DAC. Given that $R_F=R_0 / 15$, logic 0 corresponds to 0 V , and logic 1 corresponds to 4.5 V ,
a. What is the output of the DAC?
b. What is the maximum voltage that can be outputted from the DAC?
c. What is the resolution over the range 0 to 4.5 V ?
d. Find the number of bits required in the DAC if an improved resolution of 20 mV is desired.

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Problem 43

The unsigned decimal number $215_{10}$ is inputted to an eight-bit DAC. Given that $R_F=R_0 / 255$, logic 0 corresponds to 0 V , and logic 1 corresponds to 10 V ,
a. What is the output of the DAC?
b. What is the maximum voltage that can be outputted from the DAC?
c. What is the resolution over the range 0 to 10 V ?
d. Find the number of bits required in the DAC if an improved resolution of 3 mV is desired.

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Problem 44

The circuit shown in Figure P15.44 represents a simple 4-bit digital-to-analog converter. Each switch is controlled by the corresponding bit of the digital number-if the bit is 1 the switch is up; if the bit is 0 the switch is down. Let the digital number be represented by $b_3 b_2 b_1 b_0$. Determine an expression relating $v_o$ to the binary input bits.

Lainey Roebuck
Lainey Roebuck
Numerade Educator

Problem 45

The unsigned decimal number $98_{10}$ is inputted to an eight-bit DAC. Given that $R_F=R_0 / 255$, logic 0 corresponds to 0 V and logic 1 corresponds to 4.5 V ,
a. What is the output of the DAC?
b. What is the maximum voltage that can be outputted from the DAC?
c. What is the resolution over the range 0 to 4.5 V ?
d. Find the number of bits required in the DAC if an improved resolution of 0.5 mV is desired.

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Problem 46

For the DAC circuit shown in Figure P15.46 (using an ideal op-amp), what value of $R_F$ will give an output range of $-10 \leq V_0 \leq 0 \mathrm{~V}$ ? Assume that logic $0=0 \mathrm{~V}$ and logic $1=5 \mathrm{~V}$.

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Problem 47

Explain how to redesign the circuit of Figure P15.44 so that the overall circuit is a "noninverting" device.

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Problem 48

The circuit of Figure P15.48 has been suggested as a means of implementing the switches needed for the digital-to-analog converter of Figure P15.44. Explain how the circuit works.

Lainey Roebuck
Lainey Roebuck
Numerade Educator

Problem 49

The unsigned decimal number $345_{10}$ is inputted to a 12-bit DAC. Given that $R_F=R_0 / 4,095$, logic 1 corresponds to 10 V , and $\operatorname{logic} 0$ to 0 V ,
a. What is the output of the DAC?
b. What is the maximum voltage that can be outputted from the DAC?
c. What is the resolution over the range 0 to 10 V ?
d. Find the number of bits required in the DAC if an improved resolution of 0.5 mV is desired.

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Problem 50

For the DAC circuit shown in Figure P15.46 (using an ideal op-amp), what value of $R_F$ will give an output range of $-15 \leq V_0 \leq 0 \mathrm{~V}$ ?

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03:22

Problem 51

Using the model of Figure P15.44, design a 4-bit digital-to-analog converter whose output is given by

$$
v_o=-\frac{1}{10}\left(8 b_3+4 b_2+2 b_1+b_0\right) V
$$

Kajal Gautam
Kajal Gautam
Numerade Educator

Problem 52

A data acquisition system uses a DAC with a range of $\pm 15 \mathrm{~V}$ and a resolution of 0.01 V . How many bits must be present in the DAC?

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Problem 53

A data acquisition system uses a DAC with a range of $\pm 10 \mathrm{~V}$ and a resolution of 0.04 V . How many bits must be present in the DAC?

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Problem 54

A data acquisition system uses a DAC with a range of -10 to +15 V and a resolution of 0.004 V . How many bits must be present in the DAC?

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Problem 55

A DAC is to be used to deliver velocity commands to a motor. The maximum velocity is to be $2,500 \mathrm{rev} / \mathrm{min}$, and the minimum nonzero velocity is to be $1 \mathrm{rev} / \mathrm{min}$. How many bits are required in the DAC? What will the resolution be?

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Problem 56

Assume the full-scale value of the analog input voltage to a particular analog-to-digital converter is 10 V .
a. If this is a 3-bit device, what is the resolution of the output?
b. If this is an 8 -bit device, what is its resolution?
c. Make a general comment about the relationship between the number of bits and the resolution of an ADC.

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Problem 57

The voltage range of feedback signal from a process is -5 V to +15 V , and a resolution of 0.05 percent of the voltage range is required. How many bits are required for the DAC?

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Problem 58

Eight channels of analog information are being used by a computer to close eight control loops. Assume that all analog signals have identical frequency content and are multiplexed into a single ADC . The ADC requires $100 \mu \mathrm{~s}$ per conversion. The closed-loop software requires $500 \mu \mathrm{~s}$ of computation and output time for four of the loops, and for the other four it requires $250 \mu \mathrm{~s}$. What is the maximum frequency content that the analog signal can have according to the Nyquist criterion?

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Problem 59

A rotary potentiometer is to be used as a remote rotational displacement sensor. The maximum displacement to be measured is $180^{\circ}$, and the potentiometer is rated for 10 V and $270^{\circ}$ of rotation.
a. What voltage increment must be resolved by an ADC to resolve an angular displacement of $0.5^{\circ}$ ? How many bits would be required in the ADC for full-range detection?
b. The ADC requires a $10-\mathrm{V}$ input voltage for full-scale binary output. If an amplifier is placed between the potentiometer and the ADC , what amplifier gain should be used to take advantage of the full range of the ADC?

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Problem 60

Suppose it is desired to digitize a $250-\mathrm{kHz}$ analog signal to 10 bits using a successive-approximation ADC. Estimate the maximum permissible conversion time for the ADC.

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02:06

Problem 61

A torque sensor has been mounted on a farm tractor engine. The voltage produced by the torque sensor is to be sampled by an ADC. The rotational speed of the crankshaft is $800 \mathrm{rev} / \mathrm{min}$. Because of speed fluctuation caused by the reciprocating action of the engine, frequency content is present in the torque signal at twice the shaft rotation frequency. What is the minimum sampling period that can be used to ensure that the Nyquist criterion is satisfied?

Supratim Pal
Supratim Pal
Numerade Educator

Problem 62

The output voltage of an aircraft altimeter is to be sampled using an ADC. The sensor outputs 0 V at 0 m altitude and outputs 10 V at $10,000 \mathrm{~m}$ altitude. If the allowable error in sensing ( $\pm \frac{1}{2} \mathrm{LSB}$ ) is 10 m , find the minimum number of bits required for the ADC .

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Problem 63

Consider a circuit that generates interrupts at fixed time intervals. Such a device is called a real-time clock and is used in control applications to establish the sample period as $T$ seconds for control algorithms. Show how this can be done with a square wave (clock) that has a period equal to the desired time interval between interrupts.

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Problem 64

What is the minimum number of bits required to digitize an analog signal with a resolution of:
a. $5 \%$
b. $2 \%$
c. $1 \%$

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Problem 65

A useful application that exploits the open-loop characteristics of op amps is known as a comparator. One particularly simple example known as a window comparator is shown in Figures P15.65(a) and (b). Show that $V_{\text {out }}=0$ whenever $V_{\text {low }}<V_{\text {in }}<V_{\text {high }}$ and that $V_{\text {out }}=+V$ otherwise.
a.figure cant copy
b.figure cant copy

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Problem 66

Design a Schmitt trigger to operate in the presence of noise with peak amplitude $= \pm 150 \mathrm{mV}$. The circuit is to switch around the reference value -1 V. Assume an op-amp with $\pm 10-\mathrm{V}$ supplies $\left(V_{\mathrm{st}}=8.5 \mathrm{~V}\right)$.
15.67 In the circuit of Figure P15.67, $R_1=100 \Omega$, $R_2=56 \mathrm{k} \Omega, R_i=R_1 \| R_2$, and $v_{\text {in }}$ is a $1-\mathrm{V}$ peak-to-peak sine wave. Assuming that the supply voltages are $\pm 15 \mathrm{~V}$, determine the threshold voltages (positive and negative $v^{+}$) and draw the output waveform.

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Problem 68

The circuit in Figure P15.68 shows how a Schmitt trigger might be constructed with an op-amp. Explain the operation of this circuit.

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Problem 69

Consider again the circuit of Figure P15.68. Let the op-amp be an LM741 with $\pm 15 \mathrm{~V}$ bias supplies, and suppose $R_F$ is chosen to be $104 \mathrm{k} \Omega$. Assume $V_{\text {in }}$ is a 1-kHz sinusoidal signal with $1-\mathrm{V}$ amplitude.
a. Determine the appropriate value for $R_{\mathrm{in}}$ if the output is to be high whenever $\left|V_{\text {in }}\right| \geq 0.25 \mathrm{~V}$.
b. Sketch the input and output waveforms.

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04:51

Problem 70

For the circuit shown in Figure P15.70,
a. Draw the output waveform for $v_{\text {in }}$ a $4-V$ peak-to-peak sine wave at 100 Hz and $V_{\text {ref }}=2 \mathrm{~V}$.
b. Draw the output waveform for $v_{\text {in }}$ a $4-\mathrm{V}$ peak-to-peak sine wave at 100 Hz and $V_{\text {ref }}=-2 \mathrm{~V}$.
Note that the diodes placed at the input ensure that the differential voltage does not exceed the diode offset voltage.

M Hassan Anwar
M Hassan Anwar
Numerade Educator

Problem 72

For the circuit of Figure P15.72, $v_{\text {in }}$ is a $100-\mathrm{mV}$ peak sine wave at $5 \mathrm{kHz}, R=10 \mathrm{k} \Omega$, and $D_1$ and $D_2$ are $6.2-\mathrm{V}$ Zener diodes. Draw the output voltage waveform.

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Problem 73

Show that the period of oscillation of an op-amp astable multivibrator is given by the expression

$$
T=2 R_1 C \log _e\left(\frac{2 R_2}{R_3}+1\right)
$$

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Problem 74

Use the data sheets for the 74123 monostable multivibrator to analyze the connection shown in Figure 15.60 in the text. Draw a timing diagram indicating the approximate duration of each pulse, assuming that the trigger signal consists of a positive-going transition.

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Problem 75

In the monostable multivibrator of Figure 15.61 in the text, $R_1=10 \mathrm{k} \Omega$ and the output pulse width $T=10 \mathrm{~ms}$. Determine the value of $C$.

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Problem 76

An ASCII (hex) encoded message is given below. Decode the message.

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Problem 77

An ASCII (binary) encoded message is given below. Decode the messsage. Hint: Follow a line-by-line sequence, not column-by-column.
$$
\begin{array}{llll}
1010100 & 1101000 & 1101001 & 1110011 \\
1101001 & 1101101 & 1100101 & 0101101 \\
1101110 & 1100111 & 0100000 & 1110000 \\
& & & \\
0100000 & 1101001 & 1110011 & 0100000 \\
1100011 & 1101111 & 1101110 & 1110011 \\
1110010 & 1101111 & 1100010 & 1101100 \\
1100001 & 0100000 & 1110100 & \\
1110101 & 1101101 & 1101001 & \\
1100101 & 1101101 & 0101110 &
\end{array}
$$

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04:56

Problem 78

Express the following decimal numbers in ASCII form:
a. 12
b. 345.2
c. 43.5

Sanchit Jain
Sanchit Jain
Numerade Educator

Problem 79

Express the following words in ASCII form:
a. Digital
b. Computer
c. Ascii
d. ASCII

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Problem 80

Explain why data transmission over long distances is usually done via a serial scheme rather than parallel.

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Problem 81

A certain automated data-logging instrument has 16 K -words of on-board memory. The device samples the variable of interest once every five minutes. How often must data be downloaded and the memory cleared in order to avoid losing any data?

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Problem 82

Explain why three wires are required for the handshaking technique employed by IEEE 488 bus systems.

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02:39

Problem 83

A CD-ROM can hold 650 Mbytes of information. Suppose the CD-ROMs are packed 50 per box. The manufacturer ships 100 boxes via commercial airliner from Los Angeles to New York. The distance between the two cities is 2,500 miles by air, and the airliner flies at a speed of $400 \mathrm{mi} / \mathrm{h}$. What is the data transmission rate between the two cities in bits/s?

Josh Broderick Phillips
Josh Broderick Phillips
Numerade Educator