LC circuit Oscillatiing current

[lpau001]

Homework Statement

An LC circuit is shown in the figure below. the 33 pF capacitor is initially charged by the 6V battery when S is at position a. Then S is thrown to position b so that the capacitor is shorted across the 15 mH Inductor.

Homework Equations

w= 1/sqrt(LC)

X_L = wL

x_C = 1/(wC)

The Attempt at a Solution

I didn't know where to start really, so I tried googling the problem and eventually I found that apparently

Z= |X_L - X_C|

But when I try to do these, my X_L and X_C are equal to each other, so I get 0. is this correct??

 

[gneill]

I don't see a question to be answered in the problem statement.

 

[lpau001]

ahh yea, that would make things a little difficult. Sorry.

What is the maximum value for the oscillating current assuming no resistance in the circuit?

 

[gneill]

ahh yea, that would make things a little difficult. Sorry.

What is the maximum value for the oscillating current assuming no resistance in the circuit?

And then there was light!

Look at it in terms of energy storage. When the capacitor is initially fully charged, it's holding onto all the available energy in a "static" state as electrical potential. When the charge on the capacitor is (briefly) zero, all the energy will be stored in the inductor's field with the maximum current running through it. Tie together the current and the energy.

 

[rwisz]

Yes, that is correct. In an LC circuit, when the capacitor is fully charged and then shorted across the inductor, the energy stored in the capacitor will start to discharge and create an oscillating current. This means that the reactance of the inductor (XL) and the reactance of the capacitor (XC) will be equal at certain points during the oscillation, resulting in a net reactance of 0. This is known as resonance in an LC circuit.

To analyze the oscillating current in this circuit, you can use the equation for the natural frequency of an LC circuit, w=1/sqrt(LC). This will give you the frequency at which the oscillations will occur. You can also use the equation Z=|XL-XC| to calculate the impedance of the circuit at different points during the oscillation.

Overall, an LC circuit with an oscillating current is a fundamental concept in electrical engineering and has many practical applications, such as in radio frequency circuits and electronic filters. It is important to understand the mathematics and behavior of these circuits in order to design and analyze them effectively.