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Transient in an RC CircuitAuthor: E.E. Kimberly
Assume that a constant voltage F, a resistance R, and an uncharged condenser of capacitance C are connected as in Fig. 87 (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 countervoltage which tends to reduce the current flow. The emf across the condenser is and (86) To find the expression for current at any time after the circuit is closed, it is only necessary to differentiate equation (86). Thus, or Inasmuch as when t = 0, Therefore,
(87) The graph of Fig. 87 (b) is a plot of this equation. The voltage across the resistor R at any time is or (88) The voltage across the condenser at any time, when there is a charge qy isor < (89)
Example 82.  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 (89), from which and


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