What is the Input Impedance of a Circuit at Low and High Frequencies?

[ineedmunchies]

Homework Statement

Homework Equations

I know that at low frequency the capacitor will act like an open circuit.

However, i do not know what is meant by input impedance, does this just mean the combined impedance of the components in this circuit?

The Attempt at a Solution

Assuming it is just the combined impedances of the components:
At low frequency capacitor acts as open circuit so its just two resistors in parallel, therefore $$Z_{t}$$=2($$Z_{r}$$)

At high frequencies do capacitors act like short circuits??
And then making it just $$Z_{r}$$??

EDIT:for some reason the resistor looks odd in that picture, its just an ordinary resistor.

 

[mgb_phys]

yes input impedance, means what does the circuit 'look' like to anything attached to it's input.
You have pretty much answered the question, when frequency is very high or very low when do the capacitor and inductor look like an open circuit and when do they look like a short.

 

[ineedmunchies]

Ok, Thank you.

On a similar subject:

I've been asked to put these two values in phasor form then find the average power.

v = 311 sin (200t+7) V

i = 14 sin (200t-16) A

I believe that if this was cos instead of sin, it would be 311 $$\angle7$$
and 14 $$\angle-16$$.

Does it just change the sign of the angle??