In an LC circuit where L = 2.5 mH and C = 1.8 F with anelectromagnetic oscillati

Question

In an LC circuit where L = 2.5 mH and C = 1.8 F with anelectromagnetic oscillation the maximum charge on the capacitorcurrent 0.54 C. a.) Find the natural frequency and the period of theoscillation. b.) the amplitude of the current and the total electromagneticenergy in the oscillation. In an LC circuit where L = 2.5 mH and C = 1.8 F with anelectromagnetic oscillation the maximum charge on the capacitorcurrent 0.54 C. a.) Find the natural frequency and the period of theoscillation. b.) the amplitude of the current and the total electromagneticenergy in the oscillation.

Explanation / Answer

   a.   Frequency   f0   =   1/2* (L * C)                                  =   1/ 2 * 3.14 * (2.5 * 10-3 * 1.8 *10-6)                                  =   2373.74   Hz       timeperiod   T   =   1 /f0                                  =   1/ 2373.74                                  =   4.21* 10-4   s                                  =   1/ 2373.74                                  =   4.21* 10-4   s    b.   Maximumenergy   (electromagnetic)   Umax   =   (1/2)* Q2 / C                                                                               =   0.5* (0.54 * 10-6)2 / 1.8 *10-6                                                                               =   8.10* 10-8   J       Also      Umax   =   (1/2)* L * I2       8.10 *10-8   =   0.5 * 2.5 *10-3 * I2    Current   I   =   (8.10* 10-8 / 1.25 * 10-3)                      =   8.05* 10-3   A    Maximum electromagneticenergy            Umax   =   8.10* 10-8   J    Current   I   =   (8.10* 10-8 / 1.25 * 10-3)                      =   8.05* 10-3   A    Maximum electromagneticenergy            Umax   =   8.10* 10-8   J

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