Calculate Vout/Vin for the circuit if R = 2.0 kΩ, C = 0.020 μF and V = 140 V sin(50,000t).
A)0.02
B)0.45
C)0.80
D)0.98
E)2.2

Question

Calculate Vout/Vin for the circuit if R = 2.0 kΩ, C = 0.020 μF and V = 140 V sin(50,000t). ​  ​
A)0.02 
B)0.45 
C)0.80 
D)0.98 
E)2.2

Quizplus · Accepted Answer

The circuit can be simplified to a voltage divider with a complex impedance, where Z = R - j/(ωC) and ω = 50,000 rad/s. The voltage divider formula can be used to determine Vout/Vin:

Vout/Vin = Z/(Z+R) = (R-j/(ωC))/((R-j/(ωC))+R) = (R-j/(ωC))/(2R-j/(ωC))

Substituting the given values:

Vout/Vin = (2.0 kΩ-j/(50,000*0.020 μF))/(2*2.0 kΩ-j/(50,000*0.020 μF)) = 0.45

Therefore, the best choice is B, with an explanation as given above.

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