Numerical on Differentiator Circuit

Q.  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 = 2μF respectively?

- Published on 26 Oct 15

a. -1000 π cos 2000 πt
b. -2000 π cos 2000 πt
c. -42000 π cos 2000 πt
d. -21000 πcos 2000 πt

ANSWER: -42000 π cos 2000 πt
 
Given data:
Voltage Peak Value = 7mV
Frequency = f = 1KHz
R = 1500K Ω
C = 2μF = 2 x 10-6 F

An input voltage equation of a differentiator circuit can be expressed by,

V1 = Asin2 πft
= 7 sin2π x 1000 t
= 7 sin2000π t mV

Scale Factor = -CR = - [2 x 10-6 x 15 x 105]
= - [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.

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