High School

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An electric motor runs on a D.C. source of e.m.f. 200 V and draws a current of 10 A. If the efficiency is 40%, then what is the resistance of the armature?

a. 5 Ω
b. 12 Ω
c. 120 Ω
d. 160 Ω

Answer :

The resistance of the armature in the DC electric motor is calculated using the power loss due to resistance and the current drawn, resulting in a resistance of 12 Ω. Therefore the correct answer is option B

The question asks us to calculate the resistance of the armature in a DC electric motor given the source electromotive force (e.m.f), the current drawn, and the efficiency of the motor. To find the resistance, we can use the formula for power: P = V x I, where P is power, V is voltage, and I is current. Since the motor's efficiency is 40%, the power output is 40% of the power input.

The power input is V x I = 200 V x 10 A = 2000 W, while the power output is 0.4 x 2000 W = 800 W. The power dissipated as heat can be found by subtracting the power output from the power input (2000 W - 800 W = 1200 W). This power loss is due to the resistance in the armature, which we can express as Ploss = I2 x Ra. Substituting the known values, 1200 W = (10 A)2 x Ra, yields the armature resistance Ra = 1200 W / (10 A)2 = 12 Ω. Therefore, the correct answer is (b) 12 Ω.

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