A. 10.7mH B. 40.0mH C. 63.2mH D. 94.6mH QuestionDetails: A physics 4B student wa

Question

A. 10.7mH

B. 40.0mH

C. 63.2mH

D. 94.6mH

QuestionDetails: A physics 4B student wants to measure the inductance, L, andresistance, R, of a real inductor. Using a multimeter, a 1000Hz ACsignal generator, an oscilloscope, and 1.00f capacitor, thestudent makes several measurements and observations. First amulti-meter measurement of its resistance indicates thatR=35. The student then connects the capacitor in series withthe power supply and the inductor. The voltage across the capacitorand the inductor is 19.7 Volts. The voltage across the capacitoralone is 31.8 Volts. Finally, the oscilloscope shows that thevoltage across the resistor lags the power supply voltage. Thestudents then uses the results of the measurements and observationsto determine the inductance L. What value should the student get?

A. 10.7mH

B. 40.0mH

C. 63.2mH

D. 94.6mH

Explanation / Answer

We have the impedance of the circuit Z = [R2+ (XL-XC)2] Then current in the circuit I = V/Z So voltage across the capacitor is VC =IXC or VC = VXC/Z Now XC = 1/(2fC)               = 1/[(2)(1000Hz)(1*10-6F)]                =159 Thne Z = VXC/VC             = (19.7V)(159)/(31.8V) or [R2 +(XL-XC)2] = 98.5 or [R2 + (XL-XC)2]= 9702.252 or (35)2 + (XL -159)2 = 9702.252 or (XL - 159)2 =8477.252 or XL - 159 = 92.1 or (2)(1000Hz)L = 251.1 or L = 39.96mH        ˜ 40mH So, option (B) is correct. or XL - 159 = 92.1 or (2)(1000Hz)L = 251.1 or L = 39.96mH        ˜ 40mH So, option (B) is correct.

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