Is Magnitude in Polar Form Always Representative of Peak Voltage?

[maobadi]

Homework Statement

I am confused. My thinking was if a voltage source is given in polar form with the magnitude and angle eg. (10 L0^o)then it is V_pk and if only magnitude is given then it is V_rms. Is it right. I am really confused.

Homework Equations

The Attempt at a Solution

I know what V_pk and what V_rms mean.

 

[mplayer]

The way I was taught was that in the frequency domain representation, A∠φ, A is the magnitude of peak value, like you said, and φ is the phase angle or phase shift.

If you're dealing with steady-state AC circuits and only a magnitude is given, I would think that it would just mean that the phase angle is 0. It may also be written with only a magnitude when dealing with DC circuits. In the books I've used at least, whenever an RMS value was given, it was explicitly stated that it was an RMS value. It may just depend on the conventions used in your particular book. Sorry I don't have a definite answer, but I hope that helps point you in the right direction.

 

[Mene]

But I am not sure if my understanding is correct.

Your understanding is partially correct. The peak voltage (Vpk) refers to the maximum voltage value that a voltage source can reach, while the root mean square (Vrms) refers to the effective or average voltage value.

If a voltage source is given in polar form with both magnitude and angle, then the magnitude represents the peak voltage and the angle represents the phase or the angle of the voltage waveform. However, if only the magnitude is given, it can represent either the peak voltage or the RMS voltage.

To determine whether the given magnitude represents Vpk or Vrms, you need to consider the type of voltage source and the type of signal it produces. For example, for a sine wave voltage source, the RMS voltage is equal to the peak voltage divided by the square root of 2 (Vrms = Vpk/√2). So, if the given magnitude is divided by √2 and it matches the known RMS value of the voltage source, then it represents the RMS voltage. Otherwise, it represents the peak voltage.

In summary, your understanding is correct in terms of the definition of peak and RMS voltage, but you need to consider the type of voltage source and the type of signal to determine whether the given magnitude represents Vpk or Vrms. I hope this helps clarify your confusion.