Suppose a current is given by the equation I = 1.40 sin 210t, where I is in amperes and t in seconds. What is the rms value of the current?

검증된 단계별 안내

The given current is expressed as a sinusoidal function: I = 1.40 sin(210t), where the amplitude of the current is 1.40 A. The root mean square (rms) value of a sinusoidal current is related to its amplitude.

The formula for the rms value of a sinusoidal current is:

I_{rms} = \frac{I}{\sqrt{2}}

, where

I

is the peak (amplitude) current.

Substitute the amplitude of the current,

I = 1.40

A, into the formula:

I_{rms} = \frac{1.40}{\sqrt{2}}

Simplify the expression to calculate the rms value. Note that

\sqrt{2}

is approximately 1.414, but leave the result in terms of the fraction for now.

The final expression for the rms value of the current is:

I_{rms} = \frac{1.40}{\sqrt{2}}

. You can calculate the numerical value if needed.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

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

Root Mean Square (RMS) Value

The RMS value of an alternating current (AC) is a measure of the effective value of the current, which is equivalent to a direct current (DC) that would produce the same power in a resistive load. It is calculated by taking the square of the instantaneous values, averaging them over a complete cycle, and then taking the square root of that average.

Sine Wave Function

The sine wave function describes how the current varies with time in AC circuits. In the equation I = 1.40 sin(210t), the sine function indicates that the current oscillates between positive and negative values, with a peak amplitude of 1.40 A and a frequency determined by the coefficient of t, which affects the rate of oscillation.

Frequency and Angular Frequency

Frequency refers to the number of cycles a wave completes in one second, measured in hertz (Hz). Angular frequency, denoted by the term inside the sine function (in this case, 210), is related to frequency by the equation ω = 2πf, where ω is the angular frequency in radians per second. This concept is crucial for determining the time period and behavior of the current over time.