Ch 31: Alternating Current

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 31: Alternating Current

Problem 1

Chapter 31, Problem 1

You have a special light bulb with a very delicate wire filament. The wire will break if the current in it ever exceeds 1.50 A, even for an instant. What is the largest root-mean-square current you can run through this bulb?

Verified step by step guidance

Understand that the root-mean-square (RMS) current is a measure of the effective current value for alternating current (AC) circuits. It is related to the peak current by the formula:

I

_rms=I_peak/√2.

Identify that the peak current

I

_peak is the maximum current that can flow through the filament without breaking it, which is given as 1.50 A.

Use the formula for RMS current:

I

_rms=I_peak/√2. Substitute the peak current value into the formula.

Calculate the RMS current by dividing the peak current by the square root of 2:

I

_rms=1.50/√2.

Conclude that the largest RMS current you can run through the bulb is the result of the calculation from the previous step, ensuring the current does not exceed the filament's breaking point.

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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 through a conductor, measured in amperes (A). It is crucial to understand the maximum current a device can handle to prevent damage. In this context, the filament can withstand up to 1.50 A, which is the threshold for safe operation.

Root-Mean-Square (RMS) Current

RMS current is a measure of the effective value of an alternating current (AC), equivalent to a direct current (DC) that would deliver the same power. It is calculated as the square root of the average of the squares of instantaneous current values over a cycle. For safety, the RMS current must be less than or equal to the maximum allowable current.

Alternating Current (AC)

Alternating current is a type of electrical current where the flow of electric charge periodically reverses direction. Understanding AC is essential for calculating RMS values, as AC currents vary over time, unlike direct currents which remain constant. This variation necessitates using RMS to assess the effective current safely.

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Related Practice

Textbook Question

A capacitor is connected across an ac source that has voltage amplitude 60.0 V and frequency 80.0 Hz. What is the phase angle Φ for the source voltage relative to the current? Does the source voltage lag or lead the current?

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Textbook Question

The voltage across the terminals of an ac power supply varies with time according to Eq. (31.1) v = Vcosωt. The voltage amplitude is V = 45.0 V. What are (a) the root-mean-square potential difference V_rms and (b) the average potential difference V_av between the two terminals of the power supply?

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Textbook Question

A sinusoidal current i = I cosωt has an rms value I_rms = 2.10 A. What is the current amplitude?

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