** Transient Response **

##### Transient Response

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

**Transients** = circuit responses to sudden changes in a circuit.

- The transients in the system occur because of presence of energy storage elements like inductor and capacitor
- 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.
- Inductor opposes sudden change in current
- 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.**

- Just before switching (from t = $\infty$ to t = 0$^-$)
- Just after switching (At t = 0$^+$)
- 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:

**Solved Example: 9885-09**

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:

**Solved Example: 9885-10**

While drawing vector diagram for a series circuit, the reference vector is?