A 230-V d.c. series motor has an armature circuit resistance

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A 230-V d.c. series motor has an armature circuit resistance of 0.2Ω and field resistance of 0.1Ω. At rated votage, the motor draws a line current of 40 amps and runs at speed of 1000 r.p.m. What is the speed of the motor for a line current of 20 A at 230 V? Assume that the flux at 20 A line current is 60% of the flux at 40 A line current.

1. 1213 rpm
2. 1513 rpm
3. 1713 rpm
4. 1913 rpm

Correct Option: C

For 40 A line current,
E_α1 = V_t − I_α (r_α + r_s)
= 230 – 40 (0.2 + 0.1) = 218 V
For a line current of 20 A,
E_α2 = 230 – 20 (0.3) = 224 volts
Flux at 20 A,
φ₂ = 0.6 times the flux at 40 A,
i.e. φ₂ = 0.6 φ₁

∴	E_α1	=	n₁φ₁
	E_α1		n₂φ₂

⇒	218	=	(1000)(φ₁)
	224		n₂(0.6φ₁)

⇒ n₂ =	1000 × 224
	218 × 0.6

= 1713 r.p.m.