DC CIRCUITPREPARED BY:

130400116023- Patel Nidhi Harkishnbhai

130400116036- Sharma Surabhi Chandra Deo

BE First Semester IT

ACTIVE LEARNING ASSIGNMENTS

DEPARTMENT OF ELECTRICAL ENGINEERINGSANKALCHAND PATEL COLLEGE OF

ENGINEERING,VISNAGAR

Guided BY: Prof. P. R. Bhavsar

DC Circuits

yThe circuityResistance in combinations

yKirchhoff’s RulesyRC transient circuits

dq

dWε

Work done by a battery on charge

Here AB εε

Real Battery and Single Loop circuits… What’s the current ?

Conservation of energy: Kirchoff’s first Law: Sum of voltages in a closed loop is zero.

2)( RrR

RiP

Rri

0iRir

ViRirV

2

2

R

aa

Real Circuit with ammeter and voltmeter

Equivalent ResistanceResistors in Series

Series requirements– Conservation of energy– Potential differences add– Current is constant

n21 VVVV ...Apply Ohm’s Law to each resistor

n21eq IRIRIRIR ...

n21eq RRRR ...

Resistors in parallel

Parallel requirements– Charge conservation– Currents must add– Potential difference is

same across each resistor

321 iiii

Apply Ohm’s Law to each resistor

n21eq RV

RV

RV

RV

...n21eq R1

R1

R1

R1

...

Example 1

What is current through battery?

What is current through i2 ?

Kirchhoff’s Rules1 The algebraic sum of the

currents entering a junction is zero. (Conservation of Charge)

2 The algebraic sum of the changes in electric potential difference around any closed circuit loop is zero. (Conservation of Energy)

Signs for Rule 2The direction of travel when traversing the loop is from a to b.

Problem 2

Find the currents in each of the three legs of the circuit,

321 i,i,i

Three unknowns, need three equations. Also since batteries are in there cannot reduce the resistances since none in parallel or series

Example: Applying Kirchhoff’s Rules

Apply Kirchhoff’s first rule to the three wire junction at the bottom of the diagram

0III 312

Apply Kirchhoff’s second rule to the closed path in red, traversing it clockwise

0I05I03V05 21 ...

Apply Kirchhoff’s second rule to the closed path in green, traversing it clockwiseNote the sign changes for some of the elements

0I07V010I03V05 31 ....

Another, example: applying Kirchhoff’s Rules

Solve the equations simultaneously for the values if I. If I is negative the current is in the opposite direction

0III 312

0I05I03V05 21 ...

0I07I03V05 31 ...

A7740I

A9150I

A1410I

3

2

1

.

.

.

RC Circuits and Time dependence

Time dependence

Resistor slows down the charging of the capacitor

Time dependent behavior (transient) 2 cases: switch at

“a” or at “b”

a) Chargingb) discharging

In position “a” Charging the Capacitor

Use Kirchhoff’s Loop rule

Or the voltage across capacitor is …..

RCt

c

RCt

R

e1V

e1Cq

RRC

q

dt

dq

0IRq

0VV

(t)

(t)

(t)(t)

C-

- c

What’s VR across resistor?Find the current and multiply by R

,or ....

get and derivative take

(t)

(t)

(t)

(t)

1(t)

RCt

R

RCt

RCt

e

Rdt

dqV

eR

I

dt

dqI

eCq

RCt

0c

RCt

0

RCt

0

R

eVV

eCVeqq

RC

q

dt

dq

0VV

(t)

(t)

(t)(t)

c

Discharging Position b:

1. Charging the Capacitor

Note: RCis called the time constant