Does anybody know the reason why the angle 22.0°become negative -22.0° when plug into this formula P=IrmsVrms cos (φ) from the question below? Both way will give me the same answer but the reason behind the negative, I don't know.
An AC source with Vrms = 135.0 V and Irms = 11.5 A is connected to a series RLC circuit in which the current leads the voltage by 22.0°. What are the following for this circuit?
(a) total resistance R
To understand why the angle becomes negative when plugged into the formula P = IrmsVrms cos(φ), we need to have a clear understanding of the concept of phase angle and how it relates to the power factor in AC circuits.
In an AC circuit, the current and voltage waveforms are sinusoidal and can be represented as phasors in a complex plane. The phase angle (φ) represents the phase difference between the current and voltage waveforms.
When the current leads the voltage, as in this case, the phase angle is positive. This means that the current waveform reaches its maximum value before the voltage waveform does. The positive phase angle indicates that the current is ahead of the voltage in time.
However, when we use the formula P = IrmsVrms cos(φ) to calculate the power in an AC circuit, we use the cosine of the phase angle. The cosine function returns positive values for phase angles between 0° and 90° and negative values for phase angles between 90° and 180°.
In this case, the phase angle is 22.0°, which is a positive angle. But since we are calculating the power factor using the cosine function, we will get a negative value for the cosine of a positive angle between 90° and 180°.
So, in this formula, the negative sign is not indicating a negative angle. Instead, it represents the negative part of the cosine function's range for a positive angle between 90° and 180°.
To summarize, the angle becomes negative when plugged into the formula P = IrmsVrms cos(φ) because the cosine function returns negative values for a positive angle between 90° and 180°.