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: 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