If you drive the RC circuit shown with an AC source V=V0cos(t), closing the swit

Question

If you drive the RC circuit shown with an AC source V=V0cos(t), closing the switch at t=0, the resulting current is:

I(t)= Vo*( R^2 + 1/(C^2^2))^(-1/2)*cos(t+)+ (Vo/R)*(1/(1+R^2C^2^2))*e^(-t/(RC))

with =arctan(1/RC).

You do not have to derive that formula. Instead, here are some questions about interpreting this result. (In all these questions, where we say “response”, I generally mean “the amplitude of current”)

1) After a long time, is the current “leading” or “lagging” the source voltage? (Again, no calculation needed, can you just “see” the answer from the formula?)

2) Which leads to a stronger response of this circuit after a long time: low or high driver frequency? (Briefly, does this make physical sense to you, given this circuit?)

Explanation / Answer

1)After a long time the second term becomes zero. So the current has phase phi leading the voltage(in the first term).So the current leads the voltage.

2)After long time the driver frequency would be high frequency because the denominator of the first term decreases with increase in frequency so the magnitude of lower frequency would be less and that of higher frequency would be higher.

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