When does the current peak occur in an LC circuit with given values?

[gills]

Homework Statement

An LC circuit includes a 0.025$$\mu$$F capacitor and a 340$$\mu$$H inductor.

(a)If the peak voltage on the capacitor is 190 V, what is the peak current in the inductor?

(b)how long after the voltage peak does the current peak occur?

The Attempt at a Solution

I've solved part (a) already and it is 1.60A

Part (b) is where I'm stuck, but it's probably a joke.

I've figured the angular frequency out and we can find the period from that -->

T = $$\frac{2\pi}{w}$$ = 1.83$$\mu$$s

However, since there is a 90 degree difference between peak voltage and current, and there are 360 degrees in a period, I'm just dividing the value of T i have by 4 to get the time to cover one quadrant. Is this the right approach or am i off?

 

[anathema]

I commend you for trying to solve this problem and using the correct units and symbols. However, your approach for part (b) is not quite correct. Let me guide you through the correct method.

First, let's review the basics of an LC circuit. An LC circuit is a type of electrical circuit that consists of an inductor (L) and a capacitor (C) connected in series. When a voltage is applied to the circuit, the capacitor stores energy in the form of an electric field, while the inductor stores energy in the form of a magnetic field. The energy is constantly being exchanged between the two components, resulting in a periodic oscillation of voltage and current.

Now, let's look at the formula for the angular frequency (w) of an LC circuit:

w = 1/\sqrt{LC}

where L is the inductance in henries (H) and C is the capacitance in farads (F). In your case, the values given are in microfarads (μF) and microhenries (μH), so you will need to convert them to the correct units before plugging them into the formula.

Once you have calculated the angular frequency, you can use it to find the period (T) of the oscillation:

T = \frac{2\pi}{w}

This is the time it takes for one complete cycle of the oscillation. However, in this problem, we are interested in the time it takes for the current to reach its peak value after the voltage has peaked. This can be found by dividing the period by 4, as you correctly stated.

So, the correct approach is to calculate the angular frequency, then the period, and finally dividing the period by 4 to find the time it takes for the current to reach its peak value after the voltage has peaked. I hope this helps you solve the problem and understand the concept of an LC circuit better. Keep up the good work!

 

[Moetasim]

Your approach for part (b) is correct. The time it takes for the current to reach its peak after the voltage peak is one-fourth of the period, since there is a 90 degree phase difference between the voltage and current in an LC circuit. This can also be seen in the phasor diagram, where the current phasor is perpendicular to the voltage phasor. Keep in mind that this is an idealized scenario and in real circuits, there may be some resistance which will affect the phase difference and the time it takes for the current to reach its peak.