Time Constants

Author: N.H. Crowhurst

The meaning of the time constant

To understand the way in which a coupling capacitor operates, we need to know about time constants. When the voltage between the terminals of a resistance-capacitance combination (such as the coupling capacitor and grid resistor) changes, the charge across the capacitor does not change immediately. Therefore the voltage across the capacitor is initially the same as before the change. Current immediately starts to flow in the resistor, because all the change in voltage appears across it. This will determine the initial current according to I=E/R. If a current of this size continued to flow, it would take a certain time to change the charge on the capacitor, equalising the voltage across it. In seconds, the time would be given by t = C X E/L

Because the current is also determined by the voltage change, E, that started it, the time can be written as t = RC. This now eliminates both E and I from the formula, which shows that the time would be the same whatever the voltage change involved. (A larger voltage change would produce a larger current, hence the time for the charge to change would be the same.)

The time constant is numerically equal to the resistance times capacitance

However, the current does not remain constant until the voltage equalizes, and then stops. The flowing of current causes a rise in the voltage across the capacitor and a corresponding fall in the voltage across the resistor. This, in turn, causes the current in the resistor to decrease. The current thus drops off gradually before the change in voltage is complete. In fact, in the time it would take to make the whole change if the starting current were maintained, the change actually reaches only 0.637 of its complete change. In theory it never does quite reach the complete change, because the current keeps falling off indefinitely, and so does the voltage difference.

Shape of the time constant curve