For ac circuit shown in figure, R = 100 k and C = 100 pF and the phase difference between Vin and (VB - VA) is 90 . The input signal frequency is 10x rad/sec, where 'x' is . [figure]
Answer
5
Solution
Let Vin = V and a = RC. Each branch is an R–C divider across the source.
Left branch (R on top, C below): VA = V 1/(j C)R + 1/(j C) = V1 + ja
Right branch (C on top, R below): VB = V RR + 1/(j C) = jaV1 + ja
⇒ VB - VA = V ja - 11 + ja
Phase of (VB - VA) relative to Vin:
= (180 - -1a) - -1a = 180 - 2 -1a
= 90 ⇒ -1a = 45 ⇒ RC = 1
⇒ = 1RC = 1(100 103)(100 10-12)
= 105 rad/s
∴ x = 5
Answer: 5