V 1 = 2 ( 16 ) s i n ( w t ) V_1=\sqrt2(16)sin(wt) V 1 = 2 ( 16 ) s in ( wt )
V 2 = 2 4 s i n ( w t + 90 ° ) V_2=\sqrt24sin(wt+90°) V 2 = 2 4 s in ( wt + 90° )
V 3 = 2 ( 15 ) s i n ( w t − 90 ° ) V_3=\sqrt2(15)sin(wt-90°) V 3 = 2 ( 15 ) s in ( wt − 90° )
V = V R M S s i n ( w t + ϕ ) V=V_{RMS}sin(wt+\phi) V = V RMS s in ( wt + ϕ )
V = 16 s i n ( w t + 0 ) + 24 s i n ( w t + 90 ) + 15 s i n ( w t − 90 ) V=16sin(wt+0)+24sin(wt+90)+15sin(wt-90) V = 16 s in ( wt + 0 ) + 24 s in ( wt + 90 ) + 15 s in ( wt − 90 )
V 1 = 16 / ( θ = 0 ° ) ; V 2 = 24 / ( θ = 90 ° ) ; V 3 = 15 / ( θ = − 90 ° ) V_1=16/(\theta=0°);V_2=24/(\theta=90°);V_3=15/(\theta=-90°) V 1 = 16/ ( θ = 0° ) ; V 2 = 24/ ( θ = 90° ) ; V 3 = 15/ ( θ = − 90° ) Now resultant voltage
V = V 1 + V 2 + V 3 V=V_1+V_2+V_3 V = V 1 + V 2 + V 3
V = ( V 1 = 16 / ( θ = 0 ° ) ; V 2 = 24 / ( θ = 90 ° ) ; V 3 = 15 / ( θ = − 90 ° ) ) V=(V_1=16/(\theta=0°);V_2=24/(\theta=90°);V_3=15/(\theta=-90°)) V = ( V 1 = 16/ ( θ = 0° ) ; V 2 = 24/ ( θ = 90° ) ; V 3 = 15/ ( θ = − 90° ))
V = 16 ( c o s 0 ° + s i n 0 ° ) + 24 ( c o s 90 ° + s i n 90 ° ) + 15 ( s i n ( − 90 ° ) + c o s ( − 90 ° ) ) V=16(cos0°+sin0°)+24(cos90°+sin90°)+15(sin(-90°)+cos(-90°)) V = 16 ( cos 0° + s in 0° ) + 24 ( cos 90° + s in 90° ) + 15 ( s in ( − 90° ) + cos ( − 90° )) V = 16 + 0 − 15 + j ( 0 + 24 + 0 ) V=16+0-15+j(0+24+0) V = 16 + 0 − 15 + j ( 0 + 24 + 0 )
V=1+j(24)
Converting poler form
V=5+j24
Resultant velocity
V = 5 2 s i n ( w t + 24 ° ) V=5\sqrt{2}sin(wt+24°) V = 5 2 s in ( wt + 24° )
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