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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

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

(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

Inasmuch as

when t = 0,

Therefore,

(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

(8-8)

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

or <

(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

Last Update: 2010-10-06