Electrical Engineering is a free introductory textbook to the basics of electrical engineering. See the editorial for more information.... 
Home Electrical Transients Current Transient when RL Circuit is Closed  
Search the VIAS Library  Index  
Current Transient when RL Circuit is ClosedAuthor: E.E. Kimberly If the resistance and inductance of Figs. 81 and 82 be connected in series, as in Fig. 83 (a), the rate of rise of current i will be affected by both circuit impedance elements simultaneously; and the result will be similar to that shown in Fig. 83 (b) when the switch is closed. At any instant after the switch is closed the voltage V must accomplish two things. It must provide one compromiss, which is the iR voltage drop across R_{1} and a second component,which is equal to the induced voltage of the inductance L. Therefore, '
(81) To derive the equation for the current at any instant after the circuit is closed, it is convenient first to rewrite the voltage equation as follows:
Multiplying by and dividing by we obtain
(82) This reduces to The current then at any time after the switch is closed is the steadystate value less the inductive transient component as shown in Fig. 83 (&).The transient component of current approaches zero exponentially with time. Theoretically, the circuit current does not reach its final value of V/R until time is infinite. In most instances, however, it will attain practically its steadystate value in a second or less.
Example 81.  A constant emf of 10 volts is applied to a coil having a resistance of 5 ohms and an inductance of 0.01 henry. How much time will elapse after the switch is closed until onehalf of the steadystate value of current is reached?
Solution.  Steadystate current iM = 10/5 = 2 amp. By equation (82), Hence, and


Home Electrical Transients Current Transient when RL Circuit is Closed 