2018-10-01_Physics_For_You

CURRENT ELECTRICITY

ELECTRIC

CURRENT

KIRCHHOFF’S

LAW

COMBINATION

OF RESISTANCE

AND ELECTRICAL

POWER

ELECTRICAL

RESISTANCE

OHM’S

LAW

GROUPING

OF

BATTERIES

Electric Current

• Rate of ow of electric charge (positive),
  I Q
  t

dQ

dt

JdS

t

===

→ ∫

Lim

∆

∆

(^0) ∆
 
.

• J is the current density which is the
  current passing through a cross-
  section of the wire.


• 
  

 

Jd.S shows current is scalar inspite

of this we represent current with an

ar row.

• Its SI unit ampere (A) and C.G.S. unit
  is emu. It is called biot (Bi)

OHM’s Law

If the physical conditions of the conductor (length,

temperature, mechanical strain etc.) remain same, then

the current owing through the conductor is directly

proportional to the potential dierence across it’s two ends

i.e., I v V Ÿ V = IR

Limitations of Ohm’s Law

It is not a universal law that

applies everywhere under all

conditions.

Temperature Dependence

• For a conductor then
  Rt = R 0 (1 + Dt + Et^2 ), Rt = R 0 (1 + Dt)

R

t t

0 =°^0

=°

=

resistance at C

RresistanceatC

,temperature

co-effi

αβ

ccients











• Temperature coecient α= − 
  −

RR

RT T

21

12 () 1

Wheatstone Bridge • Also for resistivity, ρt = ρ^0 (1 + Dt)

• In balanced condition,
  R
  R

R

R

1

2

3

4

=

• It provides a parallel method
  to determine the value of an
  unknown resistance.

Series Combination

• In series, equivalent
  resistance
  RS = R 1 + R 2 + R 3 + ....


• In series connection, the
  current through each
  resistance is same but
  voltage divides.

Parallel Combination

• In parallel, equivalent
  resistance
  1111
  RRP 12 RR 3

=+++....

• In parallel connection,
  voltage is same but current
  divides.

Potentiometer

• Principle : Fall of
  potential across any
  portion of the wire,

V v l , V = Kl

• Comparision of emfs of

two cells, ε

ε

1

2

1

2

=l

l

• Internal resistance of a
  cell,
  rR
  V

R

l

l

=− =−







ε

111

2

Meter Bridge

• To measure resistance of unknown
  resistor using balance condition of
  wheatstone bridge

R

Sl

l

R

S

l

=

−

=

=

=

1

() (^10011)
unknownresistance
shuntresistance
balanceedlength




Junction Rule
At any junction of circuit, the sum of
currents entering and leaving must
be zero. 6 I = 0.
It is based on conservation of charge.
Loop Rule
e algebraic sum of changes in
potential around any closed loop
must be zero. 6H – 6 IR = 0
It is based on conservation of energy.
Problem Solving Strategies

• Distribute current at various junctions in the circuit starting from positive
  terminal.


• Pick a point and begin to walk around a closed loop.


• Write down the voltage change for that element according to the sign
  convention.


• By applying KVL, select the required number of loops as many as unknowns
  are available and apply KVL across each loop.


• Solve the set of simultaneous equation to nd the unknowns.

Basic Features of Ohm’s Law

• Vector form of Ohm’s law,



JE=σ

where conductivity σ

ρ

=^1 and



J is the current density.

• Graph between V and I for a metallic conductor
  V

I

V

(^1) I
1
2 T^2
T 1
Slope of the line
= tanθ=—=VI R
Heretan> 12 tan
soRR 12 >>i.e.TT 12
θθ
θ θ 2
θ 1
Series Grouping

• For n identical batteries

I n

nr R r

=

+

=

=







ε ε emf

internalresistance

• If polarity of m batteries is reversed
  In=−() 2 mmε/()+R

Mixed Grouping

• For n rows of identical batteries
  with m cells in each row. en,
  R

mr

n

R

mI

Rnet

net

net net

=+

==

,

εε, ε

• In this case current through the
  external resistance is maximum
  when R mr
  n

=

Parallel Grouping

• With identical batteries :

I

R

R r

N

R

==

=+

ε

net εε

net

net

net

,

• With unidentical batteries :

ε ε

ε

net net

net

/

/

=∑

∑

()=

()

r ,

r

I

1 R

• Materials : Crystal rectiers,
  thermistors, thyristors,
  semi-conductors.


• Conditions :
  (i) At very high temperatures
  (ii) At very low temperatures
  (iii) At very high potential
  dierences.

Resistance

e property of a

substance by virtue of

which it opposes the ow

of current through it.

R l

A

m

ne

l

A

==⋅ρ

(^2) τ
Resistivity ()
It is numerically equal
to the resistance of a
substance having unit
area of cross-section
and unit length.
Current and Drift Speed

• Dri speed, v eE
  d m
  =τ


• Mobility, μ

τ

e d

v

E

e

m

==

• Current in terms of dri velocity, In= eAvd


• In terms of relaxation time W,
  R ml
  ne A

m

ne

== 22

τ

ρ

τ

and

Ohm’s law

is not

followed for

Specic resistance

of the material

of conductor

Combining series and

parallel grouping

Flow of Charge

'Q = I't (Constant I)

= ∫Idt (I = f(t))

Area under I-t graph

gives ow of charge. Electrical Energy and Power

• Heat energy developed across a resistor H = I^2 Rt


• Power PIR

V

R

==^2

2

Equivalent Power of Bulb

• Resistance of bulb, R V
  P

R

P

=∝

(^21)
or

• In parallel P = P 1 + P 2


• In series

111

12

12

PPP 12

P

PP

PP

=+ =

+

or

• In R V
  P

=

2

, V and P are rated values for that

bulb.

• In parallel, a bulb having more rated power
  glows more brightly. In series, a bulb having
  less rated power glows more brightly.