RC Circuits

When a constant voltage is suddenly applied to a series combination of a resistor R and capacitor C, the current through the resistor decays exponentially with time. The voltage across the resistor is proportional to the current (Ohm's Law), and we can write

The product T=RC is refered to as the time constant. Physically, if you start at any point in the waveform, then after a time T the signal will have decreased to 1/e (or about 37%) of the original value.

Using the Oscilloscope to Measure the Time Constant

Instructions:

• In the box on the left hand side of the picture you are given a choice of five different resistors and five different capacitors. You may coose any one resistor and any one capacitor by dragging them into position in the small circuit below the osciiloscope screen.
• Once you have selected the resistor and capacitor the oscilloscope will display the waveform. Adjust the timebase and sensitivity of the oscilloscope until the trace occupies a maximum amount of the screen both horizontally and vertically.
• Note the voltage at the beginning of the signal, and measure the time at which the voltage has dropped to 1/e of this value. This is the time constant. You can check your value here.
• (A better method) Make careful measurements of the voltage as a function of time. The plot the voltage on a semilogarithmic plot. The equation above can be re-written by taking natural logarithms of both sides

The slope of your logarithmic plot is therefore equal to the inverse of the time constant (1/RC). You can check your value for the time constant here.