Answer:
T = 25.41 Nm
Explanation:
Calculating Nsync (Synchronous Speed):
[tex]Nsync = 120f/P[/tex]
[tex]Nsync = 120 x 120 / 4\\Nsync = 3600 rpm[/tex]
[tex]Wsync = 3600 * 2\pi /180\\Wsync = 377 rad/s[/tex]
Calculating s (Slip):
[tex]s = (Nsync - Nm) / Nsync \\
[tex]s = (3600-2464)/3600\\s = 0.3156[/tex]
Calculating Vth (Thevenin Voltage):
[tex]Vth = Vph (Xm / \sqrt{Rs^{2} + (Xs+Xm)^{2} })\\Vth = 209 (76 / \sqrt{(2.3)^{2} + (1.3 + 76)^{2} }\\Vth = 205.39 V[/tex]
Calculating Rth (Thevenin Resistance):
[tex]Rth = Rs (Xm/Xs + Xm)^{2} \\Rth = 2.3 (76/1.3 + 76)^{2} \\Rth = 2.22 ohm[/tex]
Calculating Xth (Thevenin Reactance):
Xth = Xs = 1.3 ohm
Calculating Torque:
[tex]T = (3Vth^{2}Rr/s) / (Wsync[(Rth+Rr/s)^{2} + (Xth + Xr)^{2}])\\T = (3*205.39*0.7/0.3156) / 377[(2.22+0.7/0.315)^{2} + (1.3+1.8)^{2}][/tex]
T = 280699 / 377 [19.69 + 9.61]
T = 25.41 Nm
