Calculating Peak Charge and Total Energy

In summary, an LC circuit with a 550 microfarad capacitor and a 1.35 H inductor has a charge of 0 at a certain time and a current of 0.362 A. Using the equation Q=Q0cos(wt), the time when the capacitor charge reaches its peak is approximately 2.45 seconds. The total energy in the circuit is equal to the energy stored in the inductor at the time when the capacitor charge is at its peak. To find the peak charge on the capacitor, the equation Q=Q0cos(wt) can be used, with the peak charge occurring when cos(wt)=1, or when wt=0.
  • #1
ProPatto16
326
0
LC circuit!

Homework Statement



A 550 microfarad capacitor is connected across a 1.35 H inductor. At a certain time, the charge on the capacitor is zero and the current is 0.362 A.

How much later will the capacitor charge reach its peak?
What's the total energy in the circuit?
What is the peak charge on the capacitor?



i tried Q=Q0cos(wt) with Q=0 then solving for t, which gives 2.45s but i don't know what to do from there. the only equation i have for LC circuits is that one just there and w=sqrt(1/LC)

helpppp? :)
 
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  • #2
ProPatto16 said:
How much later will the capacitor charge reach its peak? ... the only equation i have for LC circuits is that one just there and w=sqrt(1/LC)

That looks like a good equation to have for the first part. I didn't check your answer, but the approach seems correct.

As far as energy and charge, remember that the energy is being alternately stored in the capacitor and the coil. At the start, all energy is in the coil. Do you know the formulae for energy in a capacitor and in a coil?
 
  • #3


for the first part this is what i did:

Q=Q0cos(wt)

at a particular time t, Q =0... which means cos(wt) =0 so (wt)=90. so t = 90/w
w = sqrt(1/LC) = 36.7 (pretty sure the unit is Hz)

so t=90/36.7 =2.45seconds.

but it says its wrong...

as for part two i only know the formula for energy stored in an inductor... buttt..

its U=0.5LI^2... so then if that's all the energy at that time t, then the energy in the capacitor is equal to that when the capacitor charge is at its peak yeah?

and one i have those two answers part 3 is easy... i just can't seem to get part a...
 
  • #4


i figured some out...

for part 1 i needed to use pi/2 instead of 90 degrees... that got the answer..

then for part 2 i found energy in inductor and then that was the answer at peak charge...

now for part 3 I am lost...

obviously using Q=Q0cos(wt) equation to find peak charge Q0 but i don't know how... coz peak charge occurs at cos(wt)=1 which wt=0?
 
  • #5




I would approach this problem by first understanding the concept of an LC circuit. An LC circuit is a type of electric circuit consisting of an inductor (L) and a capacitor (C) connected together. In this type of circuit, energy is continuously exchanged between the inductor and the capacitor.

To calculate the peak charge and total energy in this circuit, we can use the equations Q=Q0cos(wt) and w=sqrt(1/LC). Q0 represents the initial charge on the capacitor, and w represents the angular frequency of the circuit.

To find the time at which the capacitor reaches its peak charge, we can set Q=0 in the first equation and solve for t. This gives a value of 2.45 seconds, as you have correctly calculated. This means that the peak charge on the capacitor will occur 2.45 seconds after the initial charge is zero.

To find the total energy in the circuit, we can use the equation E=1/2Q0^2C, where E represents the energy and Q0 represents the initial charge. Plugging in the given values, we get a total energy of 0.067 joules.

Finally, to find the peak charge on the capacitor, we can use the equation Q=Q0cos(wt) and plug in the time we found earlier (2.45 seconds) and the values for w, C, and L. This gives a peak charge of 0.28 coulombs.

In summary, the peak charge on the capacitor will occur 2.45 seconds after the initial charge is zero, the total energy in the circuit is 0.067 joules, and the peak charge on the capacitor is 0.28 coulombs.
 

What is peak charge and total energy?

Peak charge and total energy are two important metrics used to measure the electrical energy in a system. Peak charge refers to the maximum amount of electric charge in a system, while total energy refers to the total amount of electrical energy that has been used or stored.

How do you calculate peak charge?

Peak charge can be calculated by multiplying the peak current (the highest amount of electric current in a system) by the peak time (the duration of the peak current). This will give you the total amount of electric charge during the peak.

How do you calculate total energy?

Total energy can be calculated by integrating the power over time. This means multiplying the power (measured in watts) by the time (measured in seconds) and then summing up all the values over a given period of time. This will give you the total amount of electrical energy used or stored.

Why is it important to calculate peak charge and total energy?

Calculating peak charge and total energy can provide valuable information about the efficiency and performance of a system. It can also help in determining the capacity and limitations of a system, as well as identifying any potential issues or abnormalities.

Are there any units of measurement for peak charge and total energy?

Yes, peak charge is typically measured in coulombs (C) and total energy is measured in joules (J). However, other units such as ampere-hours (Ah) and watt-hours (Wh) may also be used, depending on the specific application.

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