Phasor diagrams are graphical representations used in electrical engineering to analyze and visualize the behavior of sinusoidal electrical quantities. These diagrams help in understanding the relationship between different electrical quantities, such as voltage and current, in an AC circuit.

Phasor diagrams are typically drawn using the root mean square (RMS) value of the electrical quantities. The RMS value is a measure of the effective or average value of a sinusoidal waveform. It is calculated by taking the square root of the average of the squared values of the waveform over a complete cycle.

Explanation:

1. Phasor diagrams:
- Phasor diagrams are used to represent the magnitude and phase relationship between different sinusoidal quantities in an AC circuit.
- They are drawn as vectors, with the length of the vector representing the magnitude of the quantity and the angle representing the phase relationship.

2. RMS value:
- The RMS value of an AC waveform is a measure of its effective or average value.
- It is calculated by taking the square root of the average of the squared values of the waveform over a complete cycle.
- The RMS value is used to determine the equivalent DC value that would produce the same heating effect as the AC waveform.

3. Importance of RMS value in phasor diagrams:
- Phasor diagrams represent the steady-state behavior of sinusoidal electrical quantities.
- The RMS value is used in phasor diagrams because it accurately represents the magnitude of the quantity over a complete cycle.
- Using the RMS value ensures that the vector lengths in the phasor diagram accurately represent the magnitudes of the quantities.

4. Peak value, average value, and instantaneous value:
- The peak value represents the maximum magnitude of the waveform.
- The average value represents the average magnitude of the waveform over a complete cycle.
- The instantaneous value represents the magnitude of the waveform at a particular instant in time.
- While these values are important in certain calculations and analysis, they are not typically used in phasor diagrams.

Conclusion:
Phasor diagrams are drawn using the RMS value of sinusoidal electrical quantities because it accurately represents the magnitude of the quantity over a complete cycle. The RMS value ensures that the vector lengths in the phasor diagram accurately represent the magnitudes of the quantities. Peak value, average value, and instantaneous value are not typically used in phasor diagrams.