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?

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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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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.