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

검증된 단계별 안내

Understand the relationship between the rms value and the amplitude of a sinusoidal current. The rms (root mean square) value is a measure of the effective value of a varying current, and for a sinusoidal current, it is related to the amplitude by the formula: I_rms = I_amplitude / sqrt(2).

Identify the given values in the problem. You are provided with the rms value of the current, I_rms = 2.10 A.

Use the formula to express the amplitude in terms of the rms value: I_amplitude = I_rms * sqrt(2).

Substitute the given rms value into the formula: I_amplitude = 2.10 A * sqrt(2).

Calculate the amplitude using the expression from the previous step. This will give you the current amplitude, which is the peak value of the sinusoidal current.

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주요 개념

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

RMS Value

The root mean square (RMS) value of a sinusoidal current is a measure of the effective value of the alternating current. It is calculated as the square root of the average of the squares of the instantaneous values over one cycle. For a sinusoidal waveform, the RMS value is I_rms = I_0/√2, where I_0 is the amplitude.

Current Amplitude

Current amplitude, denoted as I_0, is the peak value of the sinusoidal current. It represents the maximum instantaneous value that the current reaches during its cycle. In the context of RMS calculations, the amplitude is crucial for determining the effective current value using the relationship I_rms = I_0/√2.

Sinusoidal Waveform

A sinusoidal waveform is a mathematical curve that describes a smooth periodic oscillation. It is characterized by its amplitude, frequency, and phase. In electrical circuits, sinusoidal currents and voltages are common, and their analysis involves understanding these parameters to determine effective values like RMS and peak amplitude.