time responseof rl and rc networks

8/3/2019 Time responseof RL and RC networks

1/5

1. TIME RESPONSE OF RL AND RC NETWROKS


2/5

5V,

50HZ,2KHZ

CIRCUIT DIAGRAM:

To CRO

1K 20 mH

I (t)

Function

Generator

TIME RESPONSE OF R-L CIRCUIT

To CRO

10K 0.01F

I (t)5V,

50HZ,

2KHZ

Function

Generator

TIME RESPONSE OF R-C CIRCUIT.


3/5

AIM:

To study the time response of current of RL and RC networks for DC input voltages and find

the time constants.

APPARATUS:

THEORY:

If a D.C. voltage of Edc volts is applied to a circuit consisting of R and L, the differential

equation obtained from Kirchoffs second law can be written as

)e1(R

EL L

Rt

dc

L

Rt

i

dc

i

dc eR

E

R

E

trss

.. (1)

The solution i(t) consists of two parts as below

trss ii)t(i iss = Steady state part of the solution, and

itr = Transient part of the solution.

If the variation of i(t) is plotted against time, it will be obtained as below.

i (t)

R

Edc

R

E632.0 dc

t

Variation of i (t) with time for a dc voltage applied.

S.NO NAME OF THE APPARATUS RANGE TYPE QTY

1 Function generator 5V,50HZ DIGITAL 1No

2 CRO DIGITAL 1No

3 Decade Resistance Box 314 1No

4 Decade Inductance Box 100mH 1No

5 Decade Capacitance Box 10Kpf 1No

6 Multi Meter 10V 1No

7 Connecting Wires


4/5

Time constant is defined as the time taken for the current to reach 0.632 times the steady state

value of current. Its value can be shown to be equal to L/R.

Consider the series circuit in which the DC voltage is applied to the circuit consists of R and

C as shown in 2.1(b).

When a DC voltage is applied to the circuit, the differential equation of the circuit using

Kirchoffs second law can be obtained as

dt)t(iC1

RiEdc . (2)

Differentiating the above equation term by term, we get

0RC

)t(i

dt

di

(or)

0C

)t(i

dt

diR

The solution of the above first order differential equation is

RC

t

dc eR

E)t(i

, WhereR

E)0(i dc

The variation of i(t) with t is obtained as below.

i(t)

Edc/R

0.368 Edc/R

t

Response of current with time

The time constant of the circuit is the time taken for the current to reach 0.368 Edc / R. Its value can be

shown to be RC seconds.


5/5

PROCEDURE:

1) Make the connections as per the circuit diagram shown in the fig 2.1(a).2) Connect the function generator to the input terminals of the trainer circuit board.3) Connect the terminals of the 1K resistor to the CRO which measures the voltage

across the resistor and hence the current in the circuit.

4) Apply a voltage of 5V squarewave voltage at a frequency of about 2KHz and notethe wave form of current in the CRO.

5) From the waveform of current in CRO, measures the time-constant as described intheory.

6) Vary the voltage applied to 8V and 10V and repeat the same procedure.7) Make connections as per the input terminals of the trainer circuit board and apply 5V

with about 2KHz frequency and square wave.

8) Connect the function generator at the input terminals of the trainer circuit board andapply 5V with about 2KHz frequency and square wave.

9) Note the waveform of current from the CRO and measure the time constant asexplained in theory.

10) Repeat the procedure given in (8) and (9) above, but with 8V and 10V applied,keeping the frequency of the square wave constant.

RESULT:

The time response of current of RL and RC networks is studied and the time constants for DC

input voltages is find out.

VIVAVOCE:

1. What is the significance of the time-constant of a circuit?

2. Plot the variation of voltage across the capacitor in the RC circuit considered in the experiment?

3. How does inductor behave at t=0, in an electrical circuit when any voltage is applied?How does

capacitor behave in the same circuit?

time responseof rl and rc networks

Documents