Five sinusoidal waves have the same frequency `500 Hz` but their amplitudes are in the ratio `2 : 1//2 : 1//2 :1:1` and their phase angles `0 , pi//6 , pi//3 , pi//2 and pi`, respectively . The phase angle of resultant wave obtained by the superposition of these five waves is

Options

A. ` 30^@ `
B. ` 45^@ `
C. ` 60 ^@ `
D. `90^@ `

Answer

B

Explanation

`y_(t)=2Asin omegat, y_(2)=A/2sin(omega+pi/2)`
`y_(3)=(A)/(2)sin(omegat=(pi)/(3)),y_4=A sin (omegat+(pi)/(2))`
`y_(s)=A sin (omegat+pi)`
By phasor diagram. `tan phi=(PQ)/(OQ)=1`
`Rightarrow phi=45^(@)`