What is C?

The angular frequency of the oscillations in an LC circuit is .0×10³ rad/s.

If L= H, what is C?

Solution:

C=µC

What is the maximum current flowing through the circuit?

In an LC circuit, the self-inductance is
L=.0×10⁻² H
and the capacitance is
C=.0×10⁻⁶ F.

At t=0, all of the energy is stored in the capacitor, which has a charge
q=×10⁻⁵ C. 

(a) What is the angular frequency ω of the oscillations in the circuit?

(b) What is the maximum current I₀ flowing through the circuit?

(c) How long does it take the capacitor to become completely discharged? t_d=?

(d) What is the capacitor charge in µC when time t = ×10⁻⁴s?

Solution:

(b) The current is at its maximum when all the energy is stored in the inductor. From the law of energy conservation:


(c) The capacitor becomes completely discharged in one-fourth of a cycle, or during a time T/4, where T is the period of the oscillations. Since

(d) q=q₀ × cos(ω t)



 ω= rad/s
  I₀= A
t_d= s
q(t)= µC

LC Angular Frequency of the Oscillations in the Circuit

In an LC circuit, the self-inductance is
L=.0×10⁻² H
and the capacitance is
C=.0×10⁻⁶ F.

At t=0, all of the energy is stored in the capacitor, which has a charge
q=×10⁻⁵ C. 

What is the angular frequency of the oscillations in the circuit?

 ω= rad/s

Problem-Solving Strategy

 When you are solving some physical problem, try to write your solution in the form of one symbolic equation, where on the left you have the symbol of an unknown physical parameter that you have to calculate, and on the right, you have symbols of only known physical parameters and known constants. Only after this step should you make substitutions on the right, replacing symbols with physical values. If you are doing multi-step calculations using intermediate calculations, write and use intermediate calculations with as many significant figures as possible.

But enter the final result using the correct number of significant figures after rounding the calculated final value. Rounding off in intermediate calculations often makes the final result incorrect. Before you enter the final result, check again what the units of the final results should be according to the text of the problem. The test system accepts as correct results only numbers obtained in expressions written in these units.

Problem 3

 Problem 3

Three identical point charges of 1 C each are located at the vertices of an equilateral triangle, and this system has a potential energy of 1 J. (There is no in our consideration of other charges or external fields)

What would be the potential energy with the same arrangement of point charges, if the charges had different values, for example, the following: -1 C, 2 C, and 3 C?

Problem 2

 When two electric charges occupy the positions shown in Figures 1 and 2, the values of the Coulomb force between the charges are known, respectively F₁ and F₂.

Find the force of the Coulomb interaction of charges when they occupy the position shown in Figure 3.

Problem 1

Two point-objects carrying the same electric charge are keeping at some distance from each other by a string, which exerts on objects only its known tension force T₁ and does not participate in electrostatic interaction.
If four such point-objects with the same as previous charges are attached to a string at the same distance from each other as before, what will be the tension T₂ in the middle of the string?