 Solution

ID: past-exam-of-the-physics-2-paper-of-the-university-of-oxford/2018/9/a/solution

H (iω) = \frac{Z _{C}}{R + Z _{C}} = \frac{1}{1 + iω RC} .

Therefore

V_{out} (t) = \frac{V _{0}}{1 + ( ω RC ) ^{2}} cos (ω t - arctan (ω RC)) .

The amplitude ratio tends to

1

and the phase shift to zero as

ω \to 0

. For

ω \to \infty

, the amplitude ratio is asymptotic to

1/ (ω RC)

and the phase shift tends to

- π /2

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