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Home Electrical Transients Discharge of a Condenser in an RC Circuit  
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Discharge of a Condenser in an RC CircuitAuthor: E.E. Kimberly When a condenser is charged to a voltage E, the charge will produce a voltage E at its terminals after the circuit is opened. If then, as shown in Fig. 88 (a), the condenser and resistance circuit is closed at S_{2}, there will be a rush of current from C through R. As the condenser thus discharges, the voltage across its terminals decreases and the decrease in discharge current is an exponential function of time, as shown in Fig. 88 (b).
By Kirchhoff's Law, when the circuit of Fig. 88 (a) is closed, equation (86) becomes Hence, andWhen Therefore, and the discharge current is
(814)
Example 83.  A condenser having a capacitance of 0.000004 farad and charged to a potential of 100 volts is connected across a resistance of 20 ohms. How much time will elapse before the voltage across the condenser reaches 50 volts?
Solution.  In this case, From equation
(814), and
If the resistance in the preceding example were 20 megohms, the time required for the condenser voltage to fall to 50 volts would be 55.4 seconds. This circuit then can be used as a time delay device in electronic control circuits, inasmuch as the charge may be "leaked" off the condenser at any desired rate. The accuracy of control is not good, however, for delays of more than a few seconds because of the low rate of change of voltage and current after about half the charge has been spent.


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