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Lab 7: RLC Resonant Circuits Only 5 more labs to go!! L When we connect a charged capacitor to an inductor oscillations will occur in the charge of the capacitor and the current through the inductor. Energy stored in the capacitor before the switch is closed: 1 E CV 2 2 When the switch is closed, charge flows (current) through the inductor. Switch C This energy exchange between the capacitor and inductor is similar to that of a mass spring system: QCAP X IL V Current continues to flow and the capacitor becomes charged again but with opposite polarity The current through the inductor will continue to flow until an energy equal to: 1 2 E LI 2 This energy is stored in the magnetic field of the inductor. Just like the mass-spring system has a frequency of oscillation, 1 f 2 k m the current and charge in the LC circuit will oscillate with a frequency: f 1 2 LC NOTE: What is the units from L x C = Henry x Farad = seconds2 If we connect a resistor in series with the capacitor and inductor the oscillations will be damped until the energy stored diminishes to zero. This is similar to if we consider friction in the mass-spring oscillating system. When a resistor is added to the circuit the resonant frequency becomes: 1 2 2 2 1 1 R 1 R 1 1 2 f f 2 2 2 LC 2 L 4 L C 4 2 L NOTE: When R 0, f reduces to: f 1 2 LC 1 2 2 2 1 1 R 1 R 1 1 2 f f 2 2 2 LC 2 L 4 L C 4 2 L y mx b f2 1 1 slope 2 L 2 4 L 4 slope 0 1 R b 2 4 2 L 2 1/C