Introduction to Electrical Systems Course Code: EE 111 Course Code: - - PowerPoint PPT Presentation

Introduction to Electrical Systems Course Code: EE 111 Course Code: EE 111 Department: Electrical Engineering Department: Electrical Engineering Instructor Name: B G Fernandes Instructor Name: B.G. Fernandes E‐mail id: bgf @ee iitb ac in E‐mail id: bgf @ee.iitb.ac.in

EE 111: Introduction to Electrical Systems B.G.Fernandes Mon, Aug 03, 2009

Lecture 5 1/7

Sub‐Topics:

• Time domain response of RL and RC circuit
• Step response of RC circuit

EE 111: Introduction to Electrical Systems B.G.Fernandes Mon, Aug 03, 2009

Lecture 5 2/7

• Source conversion:

Review

• Super‐position theorem:

I=V/R

I I I +

For a linear system, if (x1+x2) (y1+y2)

⇒

If x1 y1 & x2 y2

t

I I I = +

1 2

EE 111: Introduction to Electrical Systems B.G.Fernandes Mon, Aug 03, 2009

y , ( 1

2)

(y1 y2)

⇒

2

y2

Lecture 5 3/7

e.g.:

6

.

T H

R = Ω 4 5

( )

TH

V = × + 6 3 6 6

V 9V =9

SC N

I I A = =2

EE 111: Introduction to Electrical Systems B.G.Fernandes

SC N

I I A 2

Mon, Aug 03, 2009

Lecture 5 4/7

Determine iD

(Assume diode is ideal) (Assume diode is ideal)

Circuit is non‐linear ‘V’ across 1Ω = (2+iD) = VAB

∴ ‘i’ supplied by battery

(2 ) 4

D D

i i + = + 5 2 4

D

i + =

A l i KVL Applying KVL

5 2 10 *4 (2 ) 4

D D

i i + = + +

1

D

i A =

Mon, Aug 03, 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 5 5/7

Time domain response of RC and RL circuit

N i i l i i i i

• No transients in purely resistive circuit
• I cannot change instantaneously in an inductor
• V across a capacitor cannot change instantaneously
• V across a capacitor cannot change instantaneously

Step response: DC voltage or current Step response: DC voltage or current suddenly applied to the circuit

t

RC circuit: where τ Time constant

( )

−

= + −

c f ci f

V V V V e τ

where, τ = Time constant Circuit is assumed to attain steady state at t = 5τ Vci= capacitor voltage at t = 0, Vf is the final value

Mon, Aug 03, 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

Vci capacitor voltage at t 0, Vf is the final value

Lecture 5 6/7

Step response of R‐C circuit

0 at

c

v t = =

Case i)

0 at

c c

v t V

+

= =

V

&

R

V V V i R = =

At steady state vc= V, I = 0 ∴ VR = 0 Steady state is attained at t ≈5τ At t = T+

&

c R R c

v v v v i R R − = − = − =

At steady state, vc and i = 0. Observation: ‘i’ through ‘C’ can h i t t l

EE 111: Introduction to Electrical Systems B.G.Fernandes

change instantaneously

Mon, Aug 03, 2009

Lecture 5 7/7