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The armature circuit equation of a separately excited dc motor is

  • A.\( V = I_aR_a \) alone
  • B.\( V = E \) alone
  • C.\( V = E + I_aR_a \)
  • D.\( V = E - I_aR_a \)

Answer: C

Correct answer: \( V = E + I_aR_a \)

The applied voltage must supply the back emf and drive the current through the armature resistance:

\[ V = E + I_aR_a \]

The back emf takes almost all of it in normal running, the resistive term being a few per cent. At standstill \( E = 0 \), so the whole of \( V \) appears across \( R_a \) and the current would be enormous - which is why a starter is needed. The form with a minus sign describes the machine acting as a generator.

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