What will be the output of differentiator circuit if input sinusoidal voltage has a peak value of 7mV & frequency of 1KHz when the values of resistance and capacitors are R=1500K and C=2 μF respectively ?
a. -1000 π cos 2000 πt
b. -2000 π cos 2000 πt
c. -42000 πcos 2000 πt
d. -21000 πcos 2000 πt
Correct Answer : c. -42000 πcos 2000 πt
Explanation :Given data:
Voltage Peak Value= 7mV
Frequency= f = 1KHz
R = 1500 K Ω
C= 2 μF = 2 x 10
-6 F
An input voltage equation of a differentiator circuit can be expressed by,
V
1 = Asin2 πft
= 7 sin 2 π x 1000 t
= 7 sin 2000 π t mV
Scale Factor = -CR = - [ 2 x 10
-6 x 15 x 10
5]
= - [ 30 x 10
-1 ]
= -3
Hence, the output voltage of differentiator circuit can be evaluated as:
Vo = -3 d / dt [ 7 sin 2000 π t]
= -3 x 7 x 2000 cos 2000 π t
= -42000 π cos 2000 π t mV.
