The Time Constant

Author: J.B. Hoag

Fig. 3 I. Charging a condenser C through a resistor R. The Time Constant is RC

In the circuit of Fig. 3 I, the current i will be large when the switch is first closed. It then decreases " exponentially " with time. Similarly, when a charged condenser is first connected to a resistance (no battery in the circuit), it empties rapidly at first, then more and more slowly. In either charge or discharge of the condenser, the product RC, of R in ohms and C in farads, is known as the time constant of the circuit. For the case of discharge, the voltage will drop to 1/2.718 or approximately 37 percent of its original value in RC seconds. The accompanying Condenser Discharge Chart (Fig. 3 J) may be used to determine the quantity of electricity left in a condenser C after a certain time of discharge through a resistor R, or the amount which will flow into the condenser through the resistor during a fixed time of charging. A straight edge is used to connect the desired quantities, as indicated. Conversely, the chart may be used to determine the time, the resistance, or the capacitance when the other quantities are known.

Condenser Discharge Chart A nomographic chart for computing the charge or discharge of a condenser through a series resistor, in terms of time and the RC product By J. B. Hoag University of Chicago

Fig. 3J. From Electronics, Sept. 1937. Instructions for use: Connect resistance and capacitance values to obtain RC product. Connect RC product and time values to obtain quantity of electricity (charge) in condenser at the end of given time value. Example: One microfarad and one megohm gives RC product of unity. At the end of 0.2 second, the condenser is 20 percent charged or 80 percent discharged

In the LR circuit of Fig. 3 K, it requires L/R seconds (L in henries, R in ohms) for the current to rise to (1 -1/2.718) or approximately 63 percent of its final steady value after the switch has been closed. The ratio of L/R is called the time constant of this circuit.

Fig. 3 K. The Time Constant of an inductive-resistive circuit is L/R