Lab 221: LC Circuits
To examine LC circuit and resonance frequency
Energy can be stored either as potential energy or kinetic energy
In a LC circuit electrical potential energy is attributed to charges at rest (gathered in a capacitor)
(1) UE= , where q is a charge on a capacitor with capacitance, C
And kinetic energy is attributed to moving charges (current) and is equal to:
(2) K = LI2, where I is a current through inductor with inductance, L
At some conditions total energy, U of a system may continuously keep swapping between one kind of energy and the other - possibly creating oscillations (like with a pendulum)
In case the system is isolated and doesn’t lose (acquire) any energy - the energy is conserved
For an LC circuit consisting only inductor L and capacitor C, we have:
(3) U = + LI2 = constant
The derivative of U is then:(4) = ()()+(LI)(= 0
Since I = ,
(5) L+ = 0 And the solution is: oscillation
I(t) = Imaxsin(ωt+Φ), where ω2 =
In this laboratory, a simple electric oscillator is constructed using an inductor L and a capacitor C connected in series
The capacitor is initially charged to 5 V then discharged through the inductor
In this experiment, there are two capacitors (47 μF and 100 μF) and two inductors (23 mH current loop and 8.5 mH solenoid) that will be used in various combinations to create LC circuits oscillating at various frequencies
The capacitor you use in the experiment is an electrolytic capacitor. It should have electrode marked (+) and charge only with a positive charge
Charging an electrolytic capacitor in the reverse direction could lead to the destruction of the
dielectric and loss of capacitor functionality. Resulting heat and pressure buildup pose a hazard.
The electrolytic capacitor is right for the experiment because of their large capacitance and
consequential ability to store large quantities of energy. The storage and movement of this energy
between capacitor and inductor are the main foci of the experiment.
The sine wave amplitude decreases so fast because of the size of the damping constant, B = R/2L. The w’ and f’ take this into account, and damped current decreases proportionally to e-Bt.
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