Ch. 23 - Electric Potential

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 23 - Electric Potential

Problem 71b

Chapter 22, Problem 71b

An analog voltage signal can vary from 0 V to 5.00 V, and it is to be converted to an 8-bit binary representation. What binary number would best represent 3.47 volts?

Verified step by step guidance

Step 1: Understand the problem. The analog voltage signal ranges from 0 V to 5.00 V, and it is being converted to an 8-bit binary representation. An 8-bit binary number can represent 2^8 = 256 discrete levels. Each level corresponds to a specific voltage range.

Step 2: Calculate the resolution of the analog-to-digital converter (ADC). The resolution is the smallest voltage increment that can be represented by one binary step. This is given by dividing the voltage range by the number of levels: Resolution = (5.00 V - 0 V) / 256.

Step 3: Determine the binary level corresponding to 3.47 V. To do this, divide the given voltage (3.47 V) by the resolution calculated in Step 2. This gives the level number corresponding to 3.47 V.

Step 4: Round the level number to the nearest integer, as binary representation corresponds to discrete levels. This integer represents the binary level that best approximates 3.47 V.

Step 5: Convert the rounded level number into an 8-bit binary representation. Use the standard method of converting a decimal number to binary, ensuring the result is padded with leading zeros to make it 8 bits long.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Analog to Digital Conversion

Analog to Digital Conversion (ADC) is the process of converting continuous analog signals into discrete digital numbers. In this case, the analog voltage signal ranging from 0 V to 5 V is sampled and quantized to fit into a binary format, allowing for digital representation and processing.

Binary Representation

Binary representation is a way of expressing numbers using only two digits: 0 and 1. In an 8-bit system, numbers can range from 0 to 255, allowing for 256 distinct values. Each bit represents a power of 2, and the combination of these bits encodes the value of the analog signal.

Quantization

Quantization is the process of mapping a range of values to a finite set of values. In the context of ADC, it involves dividing the analog voltage range into discrete levels. For an 8-bit representation, the 5 V range is divided into 256 levels, with each level corresponding to a specific binary value, which determines how closely the digital representation approximates the original analog signal.

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Electric Charge

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Textbook Question

A dust particle with mass of 0.050 g and a charge of 2.0 x 10⁻⁶ C is in a region of space where the potential is given by V(x) = (2.0 V/m²) x² - (3.0 V/m³)x³. If the particle starts at x = 2.5m, what is the initial acceleration of the charge?

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Textbook Question

Two point charges are fixed 4.0 cm apart from each other. Their charges are Q₁ = Q₂ = 6.5 μC and their masses are m₁ = 2.5 mg and m₂ = 3.5 mg. If Q₁ is released from rest, what will be its speed after a very long time?

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Textbook Question

In a photocell, ultraviolet (UV) light provides enough energy to some electrons in barium metal to eject them from the surface at high speed. To measure the maximum energy of the electrons, another plate above the barium surface is kept at a negative enough potential that the emitted electrons are slowed down and stopped, and return to the barium surface. See Fig. 23–52. If the plate voltage is -3.02 V (compared to the barium) when the fastest electrons are stopped, what was the speed of these electrons when they were emitted?

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Textbook Question

Near the surface of the Earth there is an electric field of about 150 V/m which points downward. Two identical balls with mass m = 0.550 kg are dropped from a height of 2.00 m, but one of the balls is positively charged with q₁ = 650 μC, and the second is negatively charged with q₂ = -650 μC. Use conservation of energy to determine the difference in the speeds of the two balls when they hit the ground. (Neglect air resistance.)

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Textbook Question

An analog voltage signal can vary from 0 V to 5.00 V, and it is to be converted to an 8-bit binary representation. What voltage, to the nearest 0.01 V, would have a binary representation of 01110101?

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Textbook Question

Calculate the electric potential due to a tiny dipole whose dipole moment is 4.8 x 10⁻³⁰ Cm at a point 4.1 x 10⁻⁹ m away if this point is 45° above the axis but nearer the positive charge.

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