A separately excited DC generator has an armature resist

A separately excited DC generator has an armature resist ance of 0.1 Ω and negligible armature inductance. At rated field current and rated rotor speed its open-circuit voltage is 200V. When this generator is operated at half the rated speed, with half the rated field current, an un-charged 1000µF capacitor is suddenly connected across the armature terminals. Assume that the speed remains unchanged during the transient. At what time (in microsecond) after the capacitor is connected will the voltage across it reach 25V ?

	E_b2	=	N₁φ	=	0.5N₁ × 0.5φ₁
	E_b1		N₁φ₁		N₁ × φ₁

⇒ E_b2 = 0.25 × E_b1 = 0.25 × 200 = 50
τ = R × C = 0.1 × 1000μ
50 = 5000e^{-t / 100 × 10^-6}
⇒ τ = 69.3 μ sec