Question

# A classic, undriven LC circuit contains only an inductor and a capacitor and is capable of supporting applications), the oscillations can continue indefinitely without any input of energy. LC circuits often appear as parts of larger networks: a familiar example is a radio receiver, which can be tuned by varying L or C, or both, to respond to incoming electromagnetic waves of a particular frequency.a resonant oscillation of current. In the ideal case of no resistance (unrealistic in real For a LC circuit with L=200 mH and C=0.015 µF, what is the natural (resonant) angular frequency wo? What is the corresponding linear frequency f (in Hertz)? ) Defining a time variable t so that the current in our LC circuit has its maximum value at t=0, write a mathematical expression for the current I(t) in terms of Imax and mo. c) Starting from the expression for 1(t) from part (b), determine the mathematical expressions for the voltages across the inductor and capacitor: Vi(t) and Vc(t). Express the peak values VL,max and Vc,max in terms of Imax- Sketch the relative shapes of the functions I(t), V¿(t), and V(t) on the same graph. Don't worry about the amplitude – use the same maximum and minimum value for each curve- but make sure the relative phase is correct. On your plot, indicate which curve (Vcor V.)leads the current and which lags. Mark all locations on your plot where (1) the potential energy stored in the inductor is maximized and (2) the potential energy stored in the capacitor is maximized. What fraction of the circuit's energy is stored in the inductor when the capacitor's potential energy is maximized?  Fig: 1  Fig: 2  Fig: 3  Fig: 4  Fig: 5  Fig: 6