Two alternating voltage generators produce emfs of the same amplitude E0 but with a phase difference of (π/3) . The resultant e.m.f.is

Question

Two alternating voltage generators produce emfs of the same amplitude E0 but with a phase difference of (π/3) . The resultant e.m.f.is (A) E0 sin(ω t+(π/3)) (B) E0 sin(ω t+(π/6)) (C) √3 E0 sin(ω t+(π/6)) (D) √3 E0 sin(ω t+(π/2))

Tardigrade Admin · Accepted Answer

E1=E0 sin ω t;E2=E0 sin(ω t +π/3) E=E2+E1 =E0 sin(ω +π /3)+E0 sin ω t =2E0 sin(ω t +π/6) cos (π/6) =√3E0 sin(ω t+π/6)

Q. Two alternating voltage generators produce emfs of the same amplitude $E_{0}$ but with a phase difference of $\frac{π}{3}$ . The resultant e.m.f.is

$E_{0} sin (ω t + \frac{π}{3})$

$E_{0} sin (ω t + \frac{π}{6})$

$3 E_{0} sin (ω t + \frac{π}{6})$

$3 E_{0} sin (ω t + \frac{π}{2})$

$E_{1} = E_{0} sin ω t; E_{2} = E_{0} sin (ω t + π /3)$
$E = E_{2} + E_{1}$
$= E_{0} sin (ω + π /3) + E_{0} sin ω t$
$= 2 E_{0} sin (ω t + π /6) cos (π /6)$
$= 3 E_{0} sin (ω t + π /6)$

Q. Two alternating voltage generators produce emfs of the same amplitude E0​ but with a phase difference of 3π​ . The resultant e.m.f.is

E0​sin(ωt+3π​)

E0​sin(ωt+6π​)

3​E0​sin(ωt+6π​)

3​E0​sin(ωt+2π​)