?
Two D.C. shunt generators, each with armature resistance of 0.02 ohm and field resistance of 50 ohm run in parallel and supply a total current of 1000 amperes to the load circuit. If their e.m.fs. are 270 V and 265 V, their bus bar voltage will be
Answer & Solution
Correct Answer:
Option
E
The two D.C. shunt generators are running in parallel, so they share the total load current of 1000 A based on their induced e.m.fs. and internal characteristics.
Let I₁ and I₂ be the currents supplied by generators 1 and 2 respectively.
For generator 1 (E₁=270 V): Bus bar voltage V = E₁ - I₁ × 0.02
For generator 2 (E₂=265 V): Bus bar voltage V = E₂ - I₂ × 0.02
Since both are connected to the same bus bars, their bus bar voltages must be equal, so:
E₁ - 0.02 × I₁ = E₂ - 0.02 × I₂
Rearranging gives: 0.02(I₂ - I₁) = E₂ - E₁ = 265 - 270 = -5
So: I₂ - I₁ = -5 / 0.02 = -250 ⇒ I₂ = I₁ - 250
Also, total current constraint gives: I₁ + I₂ = 1000
Substituting I₂: I₁ + (I₁ - 250) = 1000 ⇒ 2I₁ - 250 = 1000 ⇒ 2I₁ = 1250 ⇒ I₁=625 A
Then I₂=625-250=375 A
Finally, bus bar voltage V can be found using either generator (using generator 1):
V = E₁ - I₁ × 0.02 = 270 - (625×0.02) = 270 -12.5= 257.5 V
Let I₁ and I₂ be the currents supplied by generators 1 and 2 respectively.
For generator 1 (E₁=270 V): Bus bar voltage V = E₁ - I₁ × 0.02
For generator 2 (E₂=265 V): Bus bar voltage V = E₂ - I₂ × 0.02
Since both are connected to the same bus bars, their bus bar voltages must be equal, so:
E₁ - 0.02 × I₁ = E₂ - 0.02 × I₂
Rearranging gives: 0.02(I₂ - I₁) = E₂ - E₁ = 265 - 270 = -5
So: I₂ - I₁ = -5 / 0.02 = -250 ⇒ I₂ = I₁ - 250
Also, total current constraint gives: I₁ + I₂ = 1000
Substituting I₂: I₁ + (I₁ - 250) = 1000 ⇒ 2I₁ - 250 = 1000 ⇒ 2I₁ = 1250 ⇒ I₁=625 A
Then I₂=625-250=375 A
Finally, bus bar voltage V can be found using either generator (using generator 1):
V = E₁ - I₁ × 0.02 = 270 - (625×0.02) = 270 -12.5= 257.5 V
Join the Discussion
Login to post a comment or share your explanation.
Login∑(Individual Field Resistances)
∑(Individual E.M.F.s×Individual Field Resistances)+Total Load Current×Total Armature Resistance
Let's calculate:
Bus Bar Voltage
=
(
270
×
50
)
+
(
265
×
50
)
+
(
1000
×
0.02
)
50
+
50
Bus Bar Voltage=
50+50
(270×50)+(265×50)+(1000×0.02)
Bus Bar Voltage
=
13500
+
13250
+
20
100
Bus Bar Voltage=
100
13500+13250+20
Bus Bar Voltage
=
26770
100
Bus Bar Voltage=
100
26770
Bus Bar Voltage
=
267.7
V
Bus Bar Voltage=267.7V
I1=Eg1-v/Ra
I2=Eg2-v/Ra
I1+I2=270-v/Ra+265-v/Ra
Solve it than we find
2v=535
V=535/2
V =267.5v
I1=Eg1-V/Ra
I2= Eg2-V/Ra
I1+I2= 270-V/Ra +265-V/Ra
Solve it than we find
2V=515
v= 257.5