Ch 27: Current and Resistance

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 27: Current and Resistance

Problem 41a

Chapter 27, Problem 41a

The electron beam inside an old television picture tube is 0.40 mm in diameter and carries a current of 50 μA. This electron beam impinges on the inside of the picture tube screen. How many electrons strike the screen each second?

Verified step by step guidance

Understand the problem: The goal is to determine how many electrons strike the screen each second. This involves using the relationship between current, charge, and time.

Recall the formula for current: \( I = \frac{Q}{t} \), where \( I \) is the current, \( Q \) is the total charge, and \( t \) is the time. Rearrange this formula to find \( Q \): \( Q = I \cdot t \).

Determine the charge of a single electron: The elementary charge \( e \) is \( 1.6 \times 10^{-19} \, \text{C} \). The total number of electrons \( n \) can be found using \( Q = n \cdot e \). Rearrange this to find \( n \): \( n = \frac{Q}{e} \).

Substitute \( Q = I \cdot t \) into \( n = \frac{Q}{e} \): \( n = \frac{I \cdot t}{e} \). Since we are calculating the number of electrons per second, set \( t = 1 \; \text{s} \).

Substitute the given values into the formula: \( I = 50 \; \mu\text{A} = 50 \times 10^{-6} \; \text{A} \) and \( e = 1.6 \times 10^{-19} \; \text{C} \). Use these values to compute \( n \) using \( n = \frac{I \cdot t}{e} \).

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Key Concepts

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

Current

Current is the flow of electric charge, measured in amperes (A). In this context, the current of 50 μA (microamperes) indicates the rate at which electrons are flowing through the beam. Since 1 ampere equals 1 coulomb per second, this means that 50 μA corresponds to 50 x 10^-6 coulombs per second.

Charge of an Electron

The charge of a single electron is approximately -1.6 x 10^-19 coulombs. This fundamental property allows us to calculate the number of electrons based on the total charge flowing per second. By knowing the total current, we can determine how many individual electrons contribute to that current.

Calculating Number of Electrons

To find the number of electrons striking the screen each second, we can use the formula: number of electrons = total charge per second / charge of one electron. By substituting the current value (in coulombs) and the charge of an electron, we can easily compute the total number of electrons impacting the screen in one second.

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Textbook Question

A sculptor has asked you to help electroplate gold onto a brass statue. You know that the charge carriers in the ionic solution are singly charged gold ions, and you've calculated that you must deposit 0.50 g of gold to reach the necessary thickness. How much current do you need, in mA, to plate the statue in 3.0 hours?

Textbook Question

Thermistors, resistors whose resistance is a sensitive function of temperature, are widely used in industry and consumer devices to measure temperature. The resistance of a thermistor at temperature T can be modeled as R=R₀exp[β(1/T−1/T₀)], where T₀ is a reference temperature, the temperatures are in K, and β is a constant with units of K. Suppose you connect a thermistor to a 10.0 V battery and measure the current through it at different temperatures. At 25.0°C, which you select as your reference temperature, the current is 10.0 mA. Raising the temperature to 30.0°C causes the current to increase to 12.5 mA. What is the value of β?

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Textbook Question

The resistance of a very fine aluminum wire with a 10 μm ×10 μm square cross section is 1000 Ω . A 1000 Ω resistor is made by wrapping this wire in a spiral around a 3.0-mm-diameter glass core. How many turns of wire are needed?

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FIGURE EX27.35 is a current-versus-potential-difference graph for a material. What is the material's resistance?

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The biochemistry that takes place inside cells depends on various elements, such as sodium, potassium, and calcium, that are dissolved in water as ions. These ions enter cells through narrow pores in the cell membrane known as ion channels. Each ion channel, which is formed from a specialized protein molecule, is selective for one type of ion. Measurements with microelectrodes have shown that a 0.30-nm-diameter potassium ion (K⁺) channel carries a current of 1.8 pA. How many potassium ions pass through if the ion channel opens for 1.0 ms?

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