### What It Shows

The current in a circuit consisting of a capacitor, inductor, and resistor will oscillate back and forth as the capacitor charges and discharges.

### How It Works

The circuit layout is shown in the figure below. Initially the knife switch links the capacitor to the battery. Switching to complete the LRC circuit allows the capacitor to discharge. The current I in the circuit increases, as does the magneic field B inside the inductor. When the capacitor charge is zero, I and B are a maximum (the energy of the circuit is now stored in the inductor). As the opposite plate of the capacitor begins to charge, I and B decrease to zero and the energy becomes stored in the cap. The process reverses and repeats, but energy loss through circuit resistance damps the oscillations.

The amount of damping can be controlled by the adjustable resistor. Critical damping is given by

R^{2} = ^{4L}/_{C}

so for the above circuit, critical damping can be obtained for R = 54kΩ. The period of oscillation for an under-damped circuit is given by

T = 2pi(LC)^{½} ≈ 1.5 seconds

### Setting It Up

The pieces of apparatus are a 22.5V Ever Ready® cell, a 10μF 330V capacitor, a resistance box, a 20,000 turn 7.5kH UNILAB ^{1} inductor coil, a knife switch, and an OHP center zero milliammeter. Capacitors of 15μF and 30μF can also be used to show the effect of changing C.

### Comments

Usually this demo is run without the external resistor, with the DC resistance in the circuit being provided by the inductor and galvanometer. This will also show that you can never create a perfect LC circuit.

1 45kH 2x 20000 turn inductor 013.401, UNILAB Ltd., Blackburn, England BB1 3BT