Constructing a Low-Pass Filter
A series L-R-C circuit is driven with AC voltage of amplitude and frequency . Define to be the amplitude of the voltage across the capacitor. The resistance of the resistor is , the capacitance of the capacitor is , and the inductance of the inductor is .
Part A
What is the ratio ?
Part A.1
Find
Assume that the amplitude of the current in the circuit is . Write down an expression for the input voltage amplitude .
Hint A.1.a How to approach the problem Hint not displayed
Hint A.1.b Combined impedance Hint not displayed
Express your answer in terms of some or all of the variables , , the reactance of the capacitor , and the reactance of the inductor .
Part A.2 Find Part not displayed
Express your answer in terms of either , , , and or , , and .
 =

For the following questions it will be useful to write the voltage ratio in the following form:

.

Part B
Which of the following statements is true in the large limit (that is, for )?
Hint B.1 Hint not displayed
 is proportional to . is proportional to . is proportional to . is close to 1.
Part C
Which of the following statements is true in the small limit (that is, for )?
Hint C.1 Hint not displayed