RC Time Constant

After the switch closes in the Figure 12.3, the voltage across the capacitor begins to rise. The voltage plotted against time is represented by an exponential curve where the exponent is – / RC as shown Figure 23. The product RC has units of time when R is in Ohms and C is in farads. When = RC, the voltage reaches 63% of its final value. The value of is called time constant.

If the capacitor starts out with a voltage v and a switch connects a resistor R across its terminals, the voltage will begin to drop following an exponential waveform also. In one time constant the voltage drops to 63% of its initial value.

Figure 12.3 Exponential Charging Curve of a Capacitor.
               

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