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Transient in an RC Circuit

Author: E.E. Kimberly

Fig. 8-7. Current Transient in RC Circuit

Assume that a constant voltage F, a resistance R, and an uncharged condenser of capacitance C are connected as in Fig. 8-7 (a). Assume also that the inductance of the circuit is zero. At the instant at which the circuit is closed, the condenser - having no charge - has no emf across it and so offers no restriction to flow of current. The circuit then acts as one of pure resistance, and the initial current is

ee_001-262.png

As current flows, however, the condenser receives a charge and there is produced a counter-voltage which tends to reduce the current flow. The emf across the condenser is

and

ee_001-263.png (8-6)

To find the expression for current at any time after the circuit is closed, it is only necessary to differentiate equation (8-6). Thus, or

ee_001-264.png

Inasmuch as

ee_001-265.png

when t = 0,

ee_001-266.png

Therefore,

ee_001-267.png (8-7)

The graph of Fig. 8-7 (b) is a plot of this equation. The voltage across the resistor R at any time is

or

ee_001-268.png (8-8)

The voltage across the condenser at any time, when there is a charge qy is

or <

ee_001-269.png (8-9)

Example 8-2. - A constant voltage of 100 volts is suddenly impressed on a series circuit of R = 20 ohms and C = 0.000004 farad. How many seconds after the circuit is closed will be required for the voltage across the condenser to rise to 50 volts?

Solution. - By equation (8-9), from which and

ee_001-270.png
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Last Update: 2010-10-06