MASTER IT QUESTION ONLY. THanks Example 31.9 The Induced Current in a Motor A mo

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MASTER IT QUESTION ONLY. THanks

Example 31.9 The Induced Current in a Motor A motor contains a coil with a total resistance of 18 52 and is supplied by a voltage of 120 V. When the motor is running at its maximum speed, the back emf is 63 V. (A) Find the current in the coil at the instant the motor is turned on. (B) Find the current in the coil when the motor has reached maximum speed. SOLVE IT (A) Find the current in the coil at the instant the motor is turned on. Conceptualize Think about the motor just after it is turned on. It has not yet moved, so there is no back emf generated. As a result, the current in the motor is high. After the motor begins to turn, a back emf is generated and the current decreases. Categorize We need to combine our new understanding about motors with the relationship between current, voltage, and resistance in this substitution problem. 120 V R 18 2 Analyze Evaluate the current in the coil from R-??1 with no back emf generated: 1= 6.666 (B) Find the current in the coil when the motor has reached maximum speed. hack120 V-63 V Analyze Evaluate the current in the coil with the maximum back emf generated: 57 V 18 2 18 2 I- 3.1666 Finalize The current drawn by the motor when operating at its maximum speed is significantly less than that drawn before it begins to turn.

Explanation / Answer

P_input = e I

so I' = I/3.9 to get P' = P/3.9

I' = 3.166/3.9 = 0.812 A

I' = (e - e_back)/R

(0.812)(18) = 120 - e_back

e_back = 105.4 Volt

(B) w'/w = e_back' / e_back

e_back = N A B w

so w'/w = 105.4 / 63 = 1.673

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