A 2000V, 100KW, 9000 rpm series connected DC motor has an armature resistance of 6Ω and a negligible field resistance.
(a) Determine the armature current at the rated load.
(b) Determine the copper loss at the rated load.
(c) Determine the mechanical loss knowing that the no-load armature current is 7 A at a speed of 9000 rpm.
(d) Determine the full load mechanical torque delivered to the load at a speed of 9000 rpm.
(e) Determine the efficiency of the motor.
a) Armature current ,"I_2=I_L+I_{sh}"
"I_2=\\frac{100*10^3}{2000}"
"=50A"
"I_{sh}=\\frac{2000}6=333.33A"
"I_a= 50A+333.33A=383.33A"
b) Copper loss
"p=I^2R=333.33^2*6=881651.3334W"
C) Mechanical loss
No load current = "7A \\space and \\space N=9000rpm"
Power output= power development across the armature
copper losses across the armature
mechanical losses
Power output "I_{full}-I_{a(full)}^2 R_a- P\\space mechanical"
P mechanical "=VI,_{full}-I_{a(full)}^2 R_a-P _{output}"
"=[(2000-7*50)*383.33]+383.33^2*6-100"
"1414.1458334 W"
d) "\\frac{2\\pi N}{60}T_{out}= Power \\space output"
"100*10^3= \\frac{2\\pi N}{60}T_{out}"
"T_{out}=100*10^3* \\frac{60}{2 \\pi *9000}"
"=106 Nm"
"\\eta =\\frac{P_{out}}{P_{in}}*100=\\frac{100*1000}{141414.8334}*100 =70.71 \\%"
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