Analysis of Circuits…. Power

Power: represents the time rate at which energy is transformed.

dwp

dt=

The transformation of 1 Joule of energy in 1 second

represents an average of 1 watt.

Charge

Charge: An electric charge is the integral of the current with respect to time:

1

0q idt=ò

A charge of 1 C is transferred in 1 s by a current of 1 A.

Current

Current: A current is a net rate of flow of positives charge:

dqi

dt=

A current of 1 A involves the transfer of a charge at the rate of 1 C per second

Voltage

Voltage: A potential developed due to rate of energy in a given rate of charge.

dwv

dq=

A charge of 1 C receives an energy of 1 J

in moving through a voltage of 1 V:

Electric filed strength

Electric Filed Strength: That is defined by the magnitude and direction of the forces f on a unit positive charge q in the electric filed.

f qE=ur ur

Magnetic Field Density

Magnetic Field Density: A magnetic filed develops in the region around a moving charge carrier or current. The intensity of the magnetic effect is determined by:

f qu xB=r r ur

Where ur

Velocity of charge

Bur

The magnetic flux density

x Symbol for cross product

Resistance

Resistance: Physical parameter of current carrying wire:

LR

Ar= W

vR

i=

1G

R=

Capacitance

Capacitance is the ability of a body to hold an electrical charge. :

2

0

1

2

v

q Cv

w Cv dv Cv

dvi C

dt

=

= =

=

ò

AC

Le=

Inductance Inductance: A physical property of a magnetic

circuit:

A

L per turnL

m=

2

0

1

2

t

div L

dt

w Li di LI

=

= =ò

Impedance

In a AC circuit the opposition to the flow of AC current is based on frequency of the signal.:

It is thereof a complex quantity:

wL

wC

wL-wC

R

z

1( )z R j L

Cw

w= + ±

Galvanometer as Ammeter/ Voltmeter

Galvanometer_diagram.svg

Using Right hand Rule Force F is developed while Flux density B from permanent magnet along with

I Current passing through the coil is present:

F I xB=ur r ur

Application of Ammeter/Voltmeter

Moving Coil Ammeter

Linear Scale due toMoving Coil

Moving Iron Ammeter

Non-linear Scale Due to

Moving Iron

Ammeter

An ammeter consists of a galvanometer with a shunt resistor. The input current iin divides with im passing through the meter and ish Passing the shunt. It is clear from Fig:

1 ( / )in

mm sh

ii

R R=

+

Design of Ammeter

If Rm=50 ohm and it is required that full scale capability of 1 mA is to measure up to 5 A:

msh m

in m

iR R

i i=

-

Rsh = 0.001*50/(5-0.001)0.01 Ohm

Voltmeter

Galvanometer is used as a voltmeter by connecting a series resistor Rse

where current remains

same but total

resistance is

extended to extend

the scale.Vin = Vm + Vse

Design of Voltmeter

A full scale 1 mA galvano 0f 50 0hm to measure 5 Volt FS:

fsse m

m

VR R

i= -

Rse = (5/0.001)- 50= 4950 Ohms

A series resistance of 4950 Ohm will enable the same to read FS 5 Volts