91Ó°ÊÓ

2 mm, 6mm and $\mathrm{Ï„}\mathrm{Ï„}\mathrm{rad}$

3 mm, 5mm and $\mathrm{Ï„}\mathrm{Ï„}\mathrm{rad}$

2 mm, 2mm and $0rad$

Hint: Construct a phasor diagram.

Use the concept of phasors and draw the circuit diagram.

Formulae are as follow:

$\stackrel{→}{y_m}=\stackrel{→}{y_{m1}}+\stackrel{→}{y_{m2}}$

Where, y is vector.

a) The amplitude of their resultant wave:

$y_{m1}=2mm,y_{m2}=6mmandâˆ\dots =\mathrm{Ï„}\mathrm{Ï„}rad$

$y_{m1}=3mm,y_{m2}=5mmandâˆ\dots =\mathrm{Ï„}\mathrm{Ï„}rad$

Draw the phasor diagram for the given amplitudes by using a vector diagram.

$y_{m1}=7mm,y_{m2}=9mmandâˆ\dots =\mathrm{Ï„}\mathrm{Ï„}rad$

Draw the phasor diagram for the given amplitudes by using a vector diagram.

Draw the phasor diagram for the given amplitudes, by using a vector diagram.

Therefore, from the phasor diagram, rank of the four pairs according to the amplitude of their resultant wave, taking the greatest first is,

$y_a=y_d>y_b=y_c$

Therefore construct the phasor diagram by using the vector diagram concept. find their resultant wave by using vector addition law and rank them, taking the greatest first.