What is the capacitance of the circuit problem.

In summary, an LC circuit with a 1mH inductor and a fully charged capacitor has its energy reduced to ½ after 2.1 ms. Using the formula C= (T^2) / (2^2 * П^2 * L), the capacitance of the circuit can be calculated to be 4.4 microfarads. The charge in the circuit varies with time according to a cosine function, Q=QoCos(wt), where w is the angular frequency.
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Homework Statement


An LC circuit consists of a 1mH inductor. The capacitor is fully charged. After 2.1 ms,
the energy in the capacitor is ½ of its original value. What is the capacitance of the
circuit?


Homework Equations


(Q/C)+ L(d^2Q/dt^2)=0

d^2Q/dt^2= -(1/LC)Q


The Attempt at a Solution



I found the above equations in my physics book but I don't know what Q would be (it says that the capacitor is fully charged but it doesn't give an actual number), or how to get into a C= ? format in order to find the capacitance. Also I'm not even sure these are the formulas I need for this problem and if they're not then I have no idea what to do.
 
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  • #2


you can try to solve the task using Thomson's formula T=2*П * root of L*C
as i understood there is given that after 2,1 ms the capacitor is half discharged and it means that it will be fully dischardged after 4,2 ms, that is 4,2*10^-3 s - it is full period of time.
transforming the formula C= (T^2) / (2^2 * П^2 * L) and the result is 4,4 micro farads.
 
  • #3


The charge varies with time according to a cosine function - Q=QoCos(wt)
w is the angular frequency.
From the fact that is 1/2 from the maximum at t=2.1 ms you can find w.
 

FAQ: What is the capacitance of the circuit problem.

1. What is capacitance?

Capacitance is a measure of a circuit's ability to store electric charge. It is determined by the material, size, and shape of the conductors in the circuit.

2. How is capacitance calculated?

The capacitance of a circuit can be calculated by dividing the amount of charge stored in the circuit by the voltage across the circuit. It is measured in units of farads (F).

3. What is the relationship between capacitance and voltage?

The capacitance of a circuit is directly proportional to the voltage across the circuit. This means that as the voltage increases, the capacitance also increases, and vice versa.

4. How does capacitance affect the behavior of a circuit?

Capacitance can affect the behavior of a circuit by storing and releasing electric charge, which can impact the voltage and current in the circuit. It can also cause a delay or phase shift in the circuit's response to changes in voltage or current.

5. What factors can affect the capacitance of a circuit?

The capacitance of a circuit can be affected by the distance between conductors, the area of the conductors, the type of material used for the conductors, and the presence of other materials or objects near the conductors that may change the electric field.

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