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in an LC Circuit

Equipment Needed Qty Signal Generator 1 Coil 1 10 μF 1 / Meter 1 BB Wires 4 Alligator Clips 4 Microsoft Excel 1

A circuit containing a capacitor and an will have a characteristic resonant frequency. That is, will tend to oscillate in the circuit, and the frequency of the oscillation depends upon the capacitance C and the inductance L, according to the equation below. 1 = = 2

휔 휋푓 An analogy can be drawn between a resonating√퐿퐶 circuit and the resonant oscillation of a weight connected to a spring, in which the oscillation depends upon the weight’s mass and spring constant. Here the capacitor in the role of the spring provides a restoring force 휔 to the current, and the inductor in the role of the weight, endows a kind of inertia to the current.

The most important use of resonant circuits is as antennae. Electromagnetic waves can induce currents in circuits, and a circuit that resonates a particular frequency will tend to absorb energy efficiently from an EM wave with that frequency. When you are talking on your cellular phone, its is tuned to a particular frequency and so is the antenna on the cell tower through which you are communicating. Thus the tower and your phone both efficiently detect (and emit) EM waves at the same frequency, and data encoded in those waves can flow between them. Experimental Setup

The circuit at left is the experimental setup. The AC source symbol represents the signal generator, which produces a oscillating the frequency and of which can be controlled. The capacitor is rated at 10 μF, but since the actual capacitance may be quite different from this, you’ll use the capacitance meter to measure it. The inductor is a small coil provided, and the meter can also be used to measure its inductance. The capacitance in and the inductance in Henrys can be used to compute f, the resonant frequency, as given by the equation above.

The procedural steps are as follows:

1. Measure the capacitance of the capacitor using the meter. 2. Measure the inductance of the coil using the meter. 3. Compute the circuit’s resonant frequency using C and L. 4. Assemble the circuit making sure that the ammeter is set to measure AC current and the 푓 knob is set to the 20m/20A setting. 5. Turn the signal generator voltage knob all the way to the left before turning it on. 6. After turning on the signal generator, set its frequency to about half the resonant frequency. 7. Set the voltage on the signal generator so that the current reads about 0.10 mA. Do not change the voltage for the rest of the measurements. 8. Record the frequency and current. 9. Increase the frequency by 50 Hz and again record the frequency and current. 10. Repeat step 8 until you’ve reached a frequency that’s about 1.5 times the resonant frequency. 11. Plot current as a function of frequency using Microsoft Excel.

The resulting graph should have a peak around the circuit’s resonant frequency as in the example below.