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Engineering Science - Research Paper Example

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Engineering Science

In a series LC circuit, resonance occurs when the Inductive Reactance (XL) is equal to the Capacitive Reactance (XC). Because XC and XL are 180 degrees out of phase the combined impedance is equal to zero. This is the point where the waveform encounters its least resistance and it will tend to oscillate at this frequency. We can calculate the values at resonance from the experiment to verify this theory.
The most obvious effect of changing the resistor value is to reduce the current flow at resonance. The current flow when R=0 ohms was .92ma. However, when the resistance was increased to 1500 ohms, the resonance current was reduced to .57ma. The current at 16HZ and 1600HZ remained nearly constant at R=0 ohms and R=1500 ohms. This is due to the capacitive reactance rising at 16HZ and the inductive reactance rising at 1600 HZ to about 10000 ohms. The increased reactance of the capacitor and inductor at these frequencies diminished the effect of the resistor.
Another effect was to alter the shape of the curve as the frequency varies from 16 to 1600 HZ. When R=0 ohms, the higher peak at resonance resulted in a sharper rate of increase and a more defined peak. When R=1500 ohms, the curve was more flattened and had a less well defined peak.
Damping is a term that describes the loss of energy in a circuit, thus causing the decay in amplitude of a series RLC resonant circuit. In an ideal series LC circuit at resonance, the resistance would theoretically be 0 ohms. Once excited, this ideal circuit would oscillate forever because there is no resistance to dissipate the energy. As resistance is added to the circuit, the resistor dissipates the energy in the form of heat and the energy in the circuit decays to 0.
A circuit can be critically damped, under damped, or over damped. A critically damped circuit will decay the energy in one cycle of the resonant frequency. An under damped circuit will have less resistance and the oscillation will decay more slowly. An over damped circuit will have a higher resistance value and the oscillation will decay to 0 in less than one cycle.
The damping resistor has no effect on the resonant frequency. Though the resonant frequency stays constant, the Q factor of the circuit is reduced at higher resistance ...Show more

Summary

Using the formula, the calculated value of the resonant frequency is 1/ 6.283 * 10-3 = 159.2 HZ. Due to limitations in the resolution of the measurement equipment, the table indicates a band of frequencies where the maximum current seems to indicate resonance…
Author : hortenseborer
Engineering Science essay example
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