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(or transient phenomenon). A transient in an electric circuit is a phenomenon that occurs during a transition from one circuit condition to another that differs from the initial condition in the amplitude, phase, shape, or frequency of the voltage acting in the circuit, the values of the parameters, or the configuration of the circuit. Transients occur chiefly when circuit elements are switched into or out of the circuit. The transients arise because the current flowing through an inductance and the voltage across a capacitance cannot be altered abruptly—that is, the energy of the electric and magnetic fields in the circuit’s capacitive and inductive elements cannot be changed instantaneously.
Theoretically speaking, a transient continues for an indefinite period because the voltage and current in an electric circuit after the closing or opening of a switch approach their final (steady-state) values asymptotically. In electrical engineering, however, a transient is considered to be ended when the voltage and current reach values differing from the steady-state values by 5 to 10 percent, a condition that occurs within a comparatively short finite interval of time. An electric circuit that is characterized by constant or periodically varying currents and voltages is said to be in a steady-state condition.
A simple example of a transient is the charging of a capacitor C (Figure 1) from a DC source (a storage battery) having an electromotive force (emf) E and an internal resistance r through a resistor R, which limits the current in the circuit. If the switch is closed at the time t = 0, the current in the circuit decreases according to an exponential law and approaches zero. Simultaneously, the voltage increases and approaches asymptotically the value of the source emf. The rate of change of the voltage and the current depend on the capacitance of the capacitor and the resistance in the circuit: the larger the capacitance and resistance, the longer the duration of the charging process. After a time interval τ = (R + r)C, called the time constant for the charging of the capacitor, the voltage across the capacitor’s plates attains the value uc = 0.6327, and the current i reaches 0.37I0, where I0 is the initial current. I0 is equal to the ratio of the emf and the resistance in the circuit. After a time interval of 5τ;, UC > 0.99E and i < 0.01I0; with an error of less than 1 percent, the transient can be regarded as having ended. During the transient, the energy of the capacitor’s electric field is increased from zero to Wc = CE2/2.
During a transient, in individual parts of a circuit there may occur voltage surges and overcurrents—that is, voltages and currents substantially greater than the steady-state voltages and currents. When equipment is not selected properly, the voltage surges can result in the breakdown of insulation in, for example, capacitors, transformers, and electrical machines. Overcurrents can cause the actuation of protective devices and the disconnection of equipment; they can burn out instruments, burn contacts, and cause mechanical damage to windings as a result of electro-dynamic stresses. Transients play an exceptionally important role in automatic control systems, pulse engineering, computer technology, measurement technology, electronics, radio engineering, and power engineering.
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B. IA. ZHUKHOVITSKII