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Chapter 10: Problem 41

An electrical engineer must design a circuit to deliver the maximum amount of current to a display tube to achieve sufficient image brightness. Within her allowable design constraints, she has developed two candidate circuits and tests prototypes of each. The resulting data (in microamperes) are as follows: $$\begin{array}{l|l}\text { Circuit 1: } & 251,255,258,257,250,251,254,250,248 \\\\\hline \text { Circuit 2: } & 250,253,249,256,259,252,260,251\end{array}$$

Short Answer

Expert verified
Circuit 2 delivers more current with a mean of 253.75 microamperes.

Step by step solution

01

Calculate the Mean Current for Circuit 1

To find the average current for Circuit 1, add all the current values and divide the sum by the total number of measurements. \[ \text{Mean of Circuit 1} = \frac{251 + 255 + 258 + 257 + 250 + 251 + 254 + 250 + 248}{9} = \frac{2274}{9} = 252.67 \text{ microamperes} \]
02

Calculate the Mean Current for Circuit 2

Similarly, for Circuit 2, add all the values and divide by the number of measurements. \[ \text{Mean of Circuit 2} = \frac{250 + 253 + 249 + 256 + 259 + 252 + 260 + 251}{8} = \frac{2030}{8} = 253.75 \text{ microamperes} \]
03

Compare the Mean Currents

Compare the mean currents calculated for Circuit 1 and Circuit 2. - Circuit 1 Mean: 252.67 microamperes - Circuit 2 Mean: 253.75 microamperes Circuit 2 has a higher mean current than Circuit 1.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mean Calculation
Calculating the mean is a fundamental part of analyzing a set of data. It's the sum of all data values divided by the number of data points. This gives us an average that represents the center point of the data set.
For example, in Circuit Design, like in the problem at hand, calculating the mean of current values helps determine which circuit design is more effective. This is important because, by examining the average current, the engineer can decide which circuit will deliver higher performance.
To compute the mean, follow these steps on any data set:
  • Add up all the data values to get a total sum.
  • Count the number of data points you have.
  • Divide the sum by the count of data points.
Using these steps for Circuit 1, we added the microampere values, divided by nine (since there are nine measurements), resulting in a mean current of 252.67 microamperes.
Electrical Engineering
Electrical Engineering involves the study and application of electricity, electronics, and electromagnetism. In this field, designing efficient circuits, like the ones in the exercise, is crucial as they determine how current flows through electronic devices. Proper circuit design ensures that devices operate at optimal performance while maintaining safety.
When engineers design circuits, they consider many parameters, such as:
  • Current flow: Too much or too little can impact performance.
  • Voltage levels: Must be managed correctly to avoid damage.
  • Frequency: Certain applications require specific frequencies for efficiency.
By understanding the parameters, an engineer can adjust designs to meet specific requirements, such as delivering maximum current to a display tube, as seen in our exercise.
Data Analysis
Data analysis is an essential skill for engineers, allowing them to make informed decisions based on empirical data. In the context of the given exercise, data analysis helps to evaluate the performance of different circuits by examining current measurements.
Data analysis generally involves steps like:
  • Collecting data: This includes gathering all relevant measurements.
  • Processing data: Calculating means or other statistics to summarize the data set.
  • Interpreting data: Understanding what the statistics tell you about your design or process.
In the exercise, after calculating the means for both Circuit 1 and Circuit 2, data analysis allows the engineer to conclude, with evidence, which circuit design better meets the brightness performance criteria for the display tube. Such analyses are crucial in engineering domains to drive design decisions.

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Most popular questions from this chapter

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