Gujarat Power Engineering and Research Institute Presentation On Discharging of Capacitor through an Inductor Developed by- Kushal Kansara ( ) Harshil Panchal ( ) Shah Jinay ( ) Guided by- Prof. Ashwin Patel (Affiliated to Gujarat Technological University) 1

L-C circuit An inductor-capacitor circuit (LC circuit) is an electric circuit composed of inductors and capacitors. A second order LC circuit is composed of one inductor and one capacitor and is the simplest type of LC circuit. A second order LC circuit, also called a resonant circuit, tank circuit, or tuned circuit consists of an inductor, represented by the ‘L’, and a capacitor, represented by the ‘C’. The circuit can act as an electrical resonator, an electrical analogue of a tuning fork, storing energy oscillating at the circuit's resonant frequency. 2

Time Domain Response In time domain, the model/system is evaluated according to the progression of it's state with time. Time domain response is the study of signals over time. In Frequency domain your model/system is analyzed according to it's response for different frequencies. Frequency domain response is the study of signals over frequency. L-C circuit in practice 3

Discharging of Capacitor through an Inductor Let us assume, Initially switch S is at ‘a’ position so capacitor gets charged at V 0. Now if we change the position of switch from ‘a’ to ‘b’, then we will find such circuit shown in figure. 4

B Circuit after switching the ‘s’, from ‘a’ to ‘b’. 5

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NOTE: From eq.(3) & (4), the second order derivative of unknown (V C / I L ) is equal to the function itself, multiplied by negative constant (-1/L.C). 7

In both cases, the second order derivative is equal to the function itself, multiplied by negative constant(-ω 2 ). Now find the constants (k,ω and θ)of eq. (5) & (6), 8

9 differentiating the eq.(7)&(7’),

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11 above equation shows the discharging voltage of capacitor. above equation shows the decaying current of inductor.

12 This is the Discharging equation of Capacitor having Inductor In parallel. The V 0 in equation indicates that capacitor starts discharging from this value of voltage(applied voltage) with time (t).

Thank you… 13