As you can see it is a combination of C and L elements. Suppose if the capacitor is initially fully charged and the switch is closed, both the current in the circuit and the charge on the capacitor oscillates between maximum and minimum values. And this is why LC circuit is referred by LC oscillations. The electrostatic energy stored in the capacitor is transferred to inductor and transformed into magnetic field energy and vice versa. This oscillation of energy or current takes places infinite times if there are no resistive elements. But in practical as the zero resistance is not possible, the current eventually dies down to zero after certain number of oscillations.
Let us consider the ideal case, when there is no resistance in the circuit. Assume that the initial charge on capacitor is Qmax and the switch is closed just after t=0.
Initially as the capacitor is fully charged the total energy U in the circuit is stored in C.Total energy U = Uc + UL
At t=0 the current in the circuit I=0 and hence energy stored in inductor is zero. After the switch is closed, the rate at which charges leave or enter the capacitor plates is equal to the current in the circuit. As the capacitor begins to discharge after the switch is closed, the energy stored in its electric ﬁeld decreases. The discharge of the capacitor establishes a current in the circuit, and thus inductor starts storing some energy in form of magnetic ﬁeld of the inductor. Hence, electric ﬁeld energy of the capacitor is transferred to the magnetic ﬁeld of the inductor. When the capacitor is fully discharged, there is zero energy stored in it. At this moment, the current reaches its maximum value, and all of the energy is transformed into magnetic field and is stored in the inductor. Now, the current continues in the same direction, decreasing in magnitude, with the inductor getting discharged and eventually capacitor becoming fully charged. But the polarity of capacitor plates is now opposite to the initial polarity. This is followed by another discharge until the circuit returns to its original state of maximum charge Q and the plate polarity The oscillations of the LC circuit are analogous to the mechanical oscillations of the spring mass system. Many of those concepts are applicable to LC oscillations.
Similarly, we will also cover RLC Circuits.
We now consider a practical circuit consisting of an inductor, capacitor and a resistor connected in series. Let us assume that the initial charge on capacitor is Qmax before the switch is closed.
Once the switch is closed and a current is set up, the total energy stored in the capacitor and inductor can be found out by previously derived equations. But in this case, the total energy of the circuit is not constant, like it was in LC circuit. This is because of the resistor element in the circuit, which causes energy dissipation across it in for of heat and radiations. As the energy loss across the resistance is
given by -I2R.
Related Tutorials ( Introduction to Electrical Circuits - DC ) :