# Study the transient response of a series RC circuit

## Aim

Study the transient response of a series RC circuit and understand the time constant concept.

## Apparatus

Breadboard, Resistor, Capacitor, CRO, Function generator, CRO probes and Connecting wires.

## Theory

In this experiment you will apply a pulse waveform to the RC circuit to analyse the transient response of the circuit. The pulse-width relative to a circuit’s time constant determines how it is affected by an RC circuit. Figure 1: Experimental set-up for Transient response of RC series circuit

Time Constant (τ): Denoted by the Greek letter tau, it represents a measure of time required for certain changes in voltages and currents in RC circuits.

Generally, when the elapsed time exceeds five time constants (5τ) after switching has occurred, the currents and voltages have reached their final value, which is also called steady-state response.

The time constant of an RC circuit is the product of equivalent capacitance and the Thevenin’s resistance as viewed from the terminals of the equivalent capacitor.

τ=RC          …(1)

A Pulse is a voltage or current that changes from one level to another and back again. If a waveform’s high time equals its low time it is called a square wave. The length of each cycle of a pulse is its period (T).

The pulse width (tp) of an ideal square wave is equal to half the time period.

f=1/2t          …(2)

From Kirchhoff’s laws, it can be shown that the charging voltage across the capacitor is given by: for Where Vin is the applied source voltage to the circuit at time t=0. The product is the time constant. The response curve is increasing and is shown in Figure 2. Figure 2: Capacitor Charging for Series Circuit with a Step Input

The discharge voltage for the capacitor is given by: for ## Procedure

On Channel 1 of the oscilloscope, you can see the input voltage, and on channel 2 the voltage across the capacitor.

τ=RC = ____ sec

∴ f=1/2tp =____ Hz

Generate a square wave on channel 1 of the signal generator with 10V amplitude peak-to-peak. The frequency will be set according to for the following three cases:

Pulse width>>5τ

Set the frequency of the output such that the capacitor has enough time to fully charge and discharge during each cycle of the square wave. So, let the pulse width be 15τ and set the frequency according to equation (2).

Pulse width =

Set the frequency such that the pulse width =5τ. Since the pulse width is =5τ, the capacitor should just be able to fully charge and discharge during each pulse cycle.

Pulse width <<

In this case the capacitor does not have time to charge significantly before it is switched to discharge, and vice versa. Let the pulse width be only in this case and set the frequency accordingly.

## Precautions

• Before circuit connection working condition of all the components must be checked.
• All the connection should be tight.
• CRO probes must be checked before use.

## Conclusion

We have observed output waveforms for different frequencies and it is observed that output voltage decreases with increase in frequency. The transient response of RC series circuit is also observed.

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