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Wave Optics

Question
CBSEENPH12039510

A diode detector is used to detect an amplitude modulated wave of 60% modulation by using a condenser of capacity 250 pico farad in parallel with a load resistance 100 kilo ohm. Find the maximum modulated frequency which could be detected by it. 

  • 10.62 MHz

  • 10.62 kHz

  • 5.31 mHz

  • 5.31 kHz

Solution

B.

10.62 kHz

The frequency is given as
straight f space equals space fraction numerator 1 over denominator 2 πμτ end fraction
straight tau space equals space RC
therefore space straight f space equals open parentheses space fraction numerator 1 over denominator 2 πRC end fraction close parentheses
μ =0.6
R = 100 k = 100 x1000 Ω
c = 250 pico farad = 250 x 10-12 F
So,
straight f space equals space fraction numerator 1 over denominator 2 straight pi space straight x space 0.6 space straight x space 1000 space straight x 100 space straight x 250 space straight x 10 to the power of negative 12 end exponent end fraction
rightwards double arrow
straight f equals space fraction numerator 1 over denominator 9.42 space straight x 1 to the power of negative 5 end exponent end fraction
space equals space 0.1061 space straight x space 10 to the power of negative 5 end exponent
straight f space equals space 10.61 space kHz