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

Verified step by step guidance

1. Understand the relationship between the root mean square (rms) value of a sinusoidal current and its amplitude. The formula to relate these quantities is: I_{rms} = \frac{I}{\sqrt{2}}.
2. Rearrange the formula to solve for the amplitude I. Multiply both sides by \sqrt{2} to isolate I on one side: I = I_{rms} \times \sqrt{2}.
3. Substitute the given rms value into the equation. Replace I_{rms} in the equation with 2.10 A.
4. Calculate the product to find the amplitude I. This involves basic arithmetic with the square root of 2.
5. The result from the calculation will give you the amplitude of the sinusoidal current.

Key Concepts

RMS Value

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

Sinusoidal Current

A sinusoidal current is an alternating current that varies with time in a sinusoidal manner, described mathematically by the equation i(t) = I cos(ωt). Here, I represents the maximum amplitude, ω is the angular frequency, and t is time. This type of current is fundamental in AC circuits and is characterized by its periodic nature, which leads to specific behaviors in resistive, capacitive, and inductive components.

Amplitude

The amplitude of a sinusoidal current is the maximum value of the current, denoted as I_max. It represents the peak deviation of the current from its average value during one cycle. Understanding the amplitude is crucial for analyzing the power and energy delivered by the current in electrical systems, as it directly influences the RMS value and the overall performance of AC circuits.