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Ch. 25 - Electric Current and Resistance
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoGiancoli Douglas 5th editionCh. 25 - Electric Current and ResistanceProblema 81b
Capitolo 24, Problema 81b

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?

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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: Irms = I2, where I is the peak (amplitude) current.
Substitute the amplitude of the current, I = 1.40 A, into the formula: Irms = 1.402.
Simplify the expression to calculate the rms value. Note that 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: Irms = 1.402. You can calculate the numerical value if needed.

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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.
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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.
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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.
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