The separately excited dc motor in the figure below has

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The separately excited dc motor in the figure below has a rated armature current of 20 A and a rated armature voltage of 150 V. An ideal chopper switching at 5 kHz is used to control the armature voltage. I f L_a = 0.1 mH, R_a = 1 Ω , neglecting armature reaction, the duty ratio of the chopper to obtain 50% of the rated torque at the rated speed and the rated field current is

1. 0.4
2. 0.5
3. 0.6
4. 0.7

Correct Option: D

I_a rated = 20A
Vrated = 150V.
R_a = 1i

V = I_a R_a + E_b
150 = 20 + 6
E_b = 130V
Rated torque T = K_a φ I_a ., T α I_a
‘φ’ is constant, as it is seperately excited D.C. motor & armature reaction is also neglated.
Hence for obtaining 50% of roted torque I a should be dropped by 50% i.e.

	I_a	so I_an =	20	= 10 A
	2		2

Speed should be constant so
V_N = 130 + 10 = 140V
It is step down chopper V₀ = Vs δ
δ = duty ratio
140 = 2006
δ = 0.7