General Aspects

If any characteristic of the circuit is changed for example, if the applied voltage or the current passing through the circuit is changed, the current and the voltage drops across the branch of the circuit takes the time to change from its previous value to the new value. After this transitional period, the voltage and the current across circuit get stable and steady.

During this transitional period, the disturbance occurs in the circuit due to the sudden switching on and off or short circuit or any change in the voltage or current value. The current develop in the circuit because of this disturbance which is called transient disturbance is known as transient current. The transient current is generally the measure of the stored energy in the inductor or capacitor. But since the pure resistor doesn’t store energy, there is zero transient current in the pure resistive circuit.

Single energy and double energy transients

In many practical cases, one may obtain transients that lie in one of these three categories,

  1. Single energy transient: This type of transient exhibits simple exponential decay from starting to the end, as it has only one form of energy storage.

This stored energy could be either electromagnetic or electrostatic. For example an R-C circuit

  1. Double energy transient: In this type, both the forms of energy electromagnetic as well as electrostatic are storage is present, for example, an R-L-C circuit.

This transient could be aperiodic or damped Sine Wave.

  1. A combination of 1 and 2.

D.C. Transients

 

R-L Transient

In the above diagram of a circuit, having a resistor (R) and inductor (L), with an ideal voltage source(vs), and the switch (S). The below graph shows how current changes in this R-L circuit with respect to time when this switch is on at time t=0. This could be represented by the following equation.

i = V / R [1 –e –(R / L)t]

R-C transients

The below figure depicts R-C transient

Pc = V2 / V2 / R (e –t / RC –e 2t / RC)

Where p= Power in capacitor

V= Voltage

R= resistor

R-L-C transients

The above figure shows an RLC transient, in this for solving I=current, the following three cases could be considered

Case1 (R / 2L) 2  > 1 / LC

Case 2 (R / 2L)2 = 1 / LC

Case 3   (R / 2L)2 < 1 / LC

 

A.C. transients

R-L sinusoidal transient

A resistor-inductor circuit is an electric circuit composed of resistance and inductor. Now consider an RL circuit driven by a sinusoidal voltage source having initial current at zero. In this case the current will be represented as,

i = e –(R / L)t [ -V max / √ R2 + w2 L2 sin  (ψ – tan  -1 wL  /R)]

Moreover, for short-circuit evaluation; the RL circuit could be generated using the following series of equations

R-C sinusoidal transient

The diagram below shows the resistor and the capacitor in the power circuit.

The exponential part of the above equation, e-(t/RC) represents the decay factor of the transient. And the second part shows the steady current which leads the voltage but the phase difference tan-1 1/ωCR.

 

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