A 220 V, 20 A, 1000 rpm, separately excited dc motor has

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A 220 V, 20 A, 1000 rpm, separately excited dc motor has an armature resistance of 2.5Ω. The motor is controlled by a step down chopper with a frequency of 1 kHz. The input dc voltage to the chopper is 250 V. The duty cycle of the chopper for the motor to operate at a speed of 600 rpm delivering the rated torque will be

1. 0.518
2. 0.608
3. 0.852
4. 0.902

Correct Option: B

For rated speed,

V = E + I _a R_a
⇒ E = V – I_a R_a = 220 – 20 × 2.5 = 170 V

For 600 rpm, E₂ =	E₁	× N₂
	N₁

=	170	× 1600 = 102 V
	1000

Since T ∝ I
therefore rated torque means rated current Now voltage applied,
V_t = E₂ + I_a R_a = 120 + 20 × 2.5 = 152 V
V₀ = δ V_in

⇒ δ =	V₀	=	152	= 0.608
	V_in		250

Alternately
V_t – I_a r_a = E_a
220 – 20 × 2.5 = E_a
E_a = 170 = Tω = T.2π(1000) ...(A)
The output of chopper, V = α V_i = α 250 [α = duty cycle]
The, 250 α – 20 × 2.5 = T.2π(600) ...(B)

	170	=	1000
	250 α - 50		600

or, α = 0.608