GATE Electrical Engineering (EE) 2021 Solved Papers

Question : 29 of 65

Marks: +1, -0

A signal generator having a source resistance of

50 Ω

is set to generate a

1 {kHz}

sinewave. Open circuit terminal voltage is

10 {V}

peak-to-peak. Connecting a capacitor across the terminals reduces the voltage to

8 {V}

peak-to-peak. The value of this capacitor is ______________

µ {F}

. (Round off to 2 decimal places.)

Solution:

V_{0}=\;{V_{S C}}/{R+V_{S C}} V_{S}

{V}_{ {o}}{/} {V}_{ {s}}= {A}=\;{1}/{1+ {SCR}}=\;{1}/{1+j ω {RC}}

\;{ {V}_{ {OP}- {P}}}/{ {V}_{ {SP}- {p}}}=\;{1}/{|1+ {j} 2 π {fRC}|}

\;{8}/{10}=\;{1}/{√{1+(2 π × 10^{3} × 50 C)^{2}}}

1+(2 π 02 × 10^{3} × 50 {C})^{2}=(10 {/} 8)^{2}=1.5625

2 π × 10^{3} × 50 C=√{0.5625}

{C}=2.38 × 10^{-6} {F}

C=2.38 µ {F}

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