Solving Oscillations in an Electrical Circuit

[Thefox14]

Homework Statement

a. What is the frequency of the current oscillation of the circuit as it is shown?

b. What is the frequency of the oscillations in electrical potential difference, V, between the two ends of the resistor in the circuit as it is shown?

c. What is the charge on the capacitor after the current has oscillated back and forth once?

Homework Equations

$$\omega$$ = 1/(sqrt[LC]) --LaTeX's sqrt wasn't working

The Attempt at a Solution

I can easily find the freq of the current oscillations using the formula above, but I can't recall what the formula is for damped freq. Once I know that, I'm fairly certain I'll be able to solve the rest.

 

[ehild]

Was the capacitor charged before closing the switch? Are you sure you wrote the problem correctly? What do current oscillation and potential difference oscillation mean?

ehild

 

[Thefox14]

Alright I found the formula for dampened oscillations. In case someone wants to know it's:
w' = w^2 - b^2

where b = R/(2L) and w = 1/sqrt[LC]

 

[gneill]

Look up the Q-factor for an LRC circuit. How's it defined?

 

[rwisz]

a. The frequency of the current oscillation can be calculated using the formula \omega = 1/(sqrt[LC]), where L is the inductance of the circuit and C is the capacitance. This formula gives the natural frequency of oscillation for a circuit with a capacitor and inductor in series.

b. The frequency of the oscillations in electrical potential difference, V, between the two ends of the resistor can also be calculated using the same formula \omega = 1/(sqrt[LC]). This is because the potential difference across the resistor is directly related to the current oscillation, which is determined by the natural frequency of the circuit.

c. To find the charge on the capacitor after one complete oscillation, we can use the formula Q = CV, where Q is the charge, C is the capacitance and V is the potential difference across the capacitor. As the potential difference oscillates, so does the charge on the capacitor, reaching its maximum and minimum values at the same frequency as the current oscillation. After one complete oscillation, the charge on the capacitor will return to its original value.