Can someone please help me with the summary part and application part, please

I have attached an example of what it should be as well as the notes.

Question:

An ac generator producing voltage with an amplitude of 10.0 V at 200.0 rad/s is connected in series with a 50.0-?50.0-? resistor, a 400.0-mH inductor, and a 200.0-?F200.0-?F capacitor. The amplitude of the current is?

Solution: 0.135 A

I =(50.0?)2+(200.0rad/s)(400.010?3H)?(200.0rad/s)(200.010?6F)21??1?

I = 0.135 A

Summary:

Application:

Example:

Here is a summary of Chapter 31 1. This chapter covers what happens in circuits where the voltage from the sources changes in time (called AC circuits). We will look at LC circuits (with an inductor and capacitor) before adding in a resistor. These are known as RLC or LCR circuits. 2. In a charged LC circuit, charge and current will oscillate back and forth. If the initial energy is stored in the electric field of the capacitor, this energy will be transformed into the magnetic energy of the inductor as the charge attempts to balance itself by moving from one side of the capacitor to the other through the inductor. The frequency of oscillation is given by:W = VLC wherewis the angular frequency and called the natural frequency of the circuit. The charge on the capacitor will vary in time according to this mathematical law: " (t) Q wow ( -t , $ ) and the current through the inductor is given by i (t) = dq(t) dt = -Qw sin (wt + ) where is the initial phase of the oscillation. 3. Since the electrical energy stored in the capacitor isUE = > and is a cosine squared function (as seen above) the magnetic energy in the inductorUB = 2 is a sine squared function (as seen above), thus the energy in the circuit oscillates back and forth between electrical and magnetic energy. The electrical and magnetic energy will be out of phase with each other. The total energy of an LC circuit will not change. 4. Adding a resistor into an LC circuit will produce damping as the resistor will dissipate some of the energy each cycle. The exact solution is fairly difficult to derive but consists of two parts; an oscillatory part where the frequency of oscillation has been shifted slightly and an exponential decay part which accounts for the fact that energy is lost during the oscillation. 5. A forced oscillation RLC circuit consists of a voltage source that oscillates with a driving frequency wa. We will apply this to a series RLC circuit, although in principle you can do this for any arrangement of components. We can analyze the maximum current that flows in the circuit by introducing a quantity known as the reactance (symbol X) for each component of the circuit. The reactance of a resistor is simply the resistance. The reactance of a capacitor is Ac = wad 1, a function of the driving frequency and capacitance. The reactance of an inductor is XL = Wd L. Ohm's law tells us the maximum current and voltage across each component. 6. The impedance (Z) of a series RLC circuit is Z = VR2 + (XL - XC)2. The current through an RLC circuit is I = " where Em is the amplitude of the driving voltage. This relationship shows that the current that flows depends on the impedance which is contains two terms (capacitive and inductive reactances) which are functions of the driving frequency. When these two reactances are equal, the current is a maximum value. This occurs at resonance of the natural frequency of the circuit given above. 7. Phasors are a way to analyze the behavior of the RLC circuit by looking at the phase of current through each component.Question: An RLC series circuit is driven by a sinusoidal emf with angular frequency wd. If Wd is increased without changing the amplitude of the emf, the current amplitude increases. If _ is the inductance, C is the capacitance, and R is the resistance, this means that Summary of Concepts: This problem uses the relationship between the amplitude of the current in the circuit and the emf amplitude to determine the correct answer. Solution: The amplitude of current is given by: Im = Z Em where the impedance of the circuit Z = \\R2 + (wal - -1 2 giving: Em Em Im = Z R2+ (wal - -1 2 If the amplitude of the current increases, the impedance decreases. The only term in the impedance that depends on the driving angular frequency is: x2 = (WaL 1 2 which decreases as Wd increases. waC This correlation can be shown as: d