##### Transient Response

1. Study the transient response of a series RC circuit.
2. Understand the time constant concept by using fluctuating signal.

Transients = circuit responses to sudden changes in a circuit.

1. The transients in the system occur because of presence of energy storage elements like inductor and capacitor
2. The energy stored in such elements (L and C) cannot change instantaneously and will oppose the sudden change in system which results in instability due to oscillation.
3. Inductor opposes sudden change in current
4. Capacitor opposes sudden change in voltage

#### Behavior of inductor in transient:

When we try to increase current in an inductor suddenly, (i.e. $\dfrac{di}{dt} = \infty$), voltage developed across it will be infty as $V_L = L\dfrac{di}{dt} = \infty$ i.e. inductor acts as open circuit (i-0 as V= $\infty$) Thus the action of sudden in current is counteracted by establishing open circuit.

#### Behavior of capacitor in transient:

When we try to increase voltage in a capacitor suddenly, (i.e. $\dfrac{dv}{dt} = \infty$), current developed across it will be infty as $I_C = C\dfrac{dv}{dt} = \infty$ i.e. capacitor acts as short circuit (v = 0 as i= $\infty$) Thus the action of sudden in voltage is counteracted by establishing short circuit.

Terminology:
1. Just before switching (from t = $\infty$ to t = 0$^-$)
2. Just after switching (At t = 0$^+$)
3. After switching: (For t >0)

###### Solved Example: 9885-01

During capacitor charging, the voltage actually rises to _________ percent of its _________ value.

###### Solved Example: 9885-02

At certain current, the energy stored in iron cored coil is 1000 J and its copper loss is 2000 W. The time constant is:

###### Solved Example: 9885-03

A 10-$\mu$F capacitor in series with a 1-M$\Omega$ resistor is connected across a 100-V DC supply. The initial rate of rise of voltage across the capacitor is:

###### Solved Example: 9885-04

What is the expression for the current in the R-C circuit?

###### Solved Example: 9885-05

Which circuit will not always produce any transients?

###### Solved Example: 9885-06

A coil having a resistance of 8 $\Omega$ and inductance of 2 H is switched across a 48 V DC supply. The time constant of the circuit and the final value of the current in the circuit, respectively are:

###### Solved Example: 9885-07

Zero initial conditions in transient analysis mean that the system is:

###### Solved Example: 9885-08

In an R-L circuit connected to an alternating sinusoidal voltage, size of transient current primarily depends on:

A resistor and a capacitor are connected in series to a 10 V DC supply through a switch. The switch is closed at t = 0, and the capacitor voltage is found to cross 0 V at t = 0.4$\tau$, where $\tau$ is the circuit time constant. The absolute value of percentage change required in the initial capacitor voltage if the zero crossing has to happen at t = 0.2$\tau$ is: