Current Electricity Importabt Notes and MCQs

Notes 53 Pages

Joint Entrance Examination (Main)

Physics

Contributed by

Gulzar Dubey

54
SOME IMPORTANT POINTS
1. Current I
dQ
dt

If current is steady, then I
Q ne
t t
 
2. If a point charge q is moving in circle with constant speed and frequency f, then corrosponding current.
I fq q
2

 

3. Current density at any point of conductor.
dI
J
da cos


dI J.da I J.da   

   
If the cross-sectional area is perpendicular to the current and if J is constant over the entire cross-
section, then
I
J
A

4. Ohm's law
V
R
I

where R= resistance
1 Ohm
volt
1
Ampere

V= potential difference
I= current flowing through the conductor
1
R
is called the conductance of material.
Its unit is
1

or mho or seimen(s)
5. Resistivity
R
A



resistivity
RA



unit

Ohm.m ( m)

Dimension formula
1 3 3 2
M L T A
 

6. Conductivity
1


 unit  mho.m
–1
1 3 3 2
Dimension M L T A
 
 
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55
7. Drift velocity
d d
eE
V and I neAV
m
  
d
I J E E V
V
neA ne ne ne ne

    
 
where,

= Number of electrons per unit volume of the conductor
A = Area of cross-section
V = Potential difference across the conductor
E = electric field inside the conductor
I = Current
J = Current density

= Specific resistance

= Conductivity
1
 

 

 
= relxation time between cons. collisan
8. Resistivity
2
m
ne


9. Mobility
d
E

 
ne

 
2
m
Unit
volt.sec

(1) For conductor
e e
n e 
(2) For Semiconductor
e e h h
n e n e   
10. Temperature Dependence of Resisitivity
 
0
0
1
 
       
 
where, 

= resistivity at a temperature

0


= resistivity at a proper reference temperature
0

 
temperature co-efficient of resistivity
0 1
(. C )

 
0
0
R R 1
 
      
 
If
1
R and
2
R are the resistance at
1
t C
and
2
t C
respectively then
1 1
2 2
R 1 t
R 1 t


 
and
 
2 1
1 2 1
R R
R t t

 

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56
11. The emf of a Cell and Terminal Voltage: when unit positive charge is driven form negative terminal
to the positive terminal due to non-elecrical forces, the energy gained by the charge (or work done by
the non-electrical forces) is called an emf (

) of a battery..
The net potential difference between the two terminals of a battery is called the terminal voltage (V).
The terminal voltage of a battery is,
V Ir 
12. Secondary Cell: The cell which can be restored to original condition by reversing chemical processes
(i.e. by recharging) are called secondary cells. e. g. lead accumulator.
13. Charging: If the secondary cell is connected to some other external d.c. source of larger emf, current
may enter the cell through the positive terminal and leave it at the negative terminal. The electrical energy
is then converted into chemical energy. This is called charging of the cell.
For the charging of a laed storage cell (lead accumulator),
2 2
V
VIt It I Rt I rt and I
r R
 
    

where I = charging current
14. Junction or branch Point: It is the point in a network at which more then two conductors (minimum
three) meet.
15. Loop: A closed circuit formed by conductors is known as loop.
16. Kirchhoff's Rules:
First rule: `` The algebraic sum of all the electric currents meeting at the junction is zero.''
I 0 
Second Rule: `` For any closed loop the algebraic sum of the products of resistances and the respective
currents flowing through them is equal to the algebraic sum of the emfs applied along the loop.''
IR  
17. Connections of Resitors:
Series Connection:
S 1 2 3 n
R R R R ...... R    
where,
S
R  Equivalent resistance of n resistors connected in series.
Parallel connection:
p l 2 3 n
1 1 1 1 1
......
R R R R R
   
where,
p
R 
Equivalent resistance of n resistors connected in parallel.
18. Series Connection of Cells: For the series connection of two cells of emfs
1
 and
2
 and internal
resistances
1
r and
2
r ,
 
eq
1 2
1 2 eq
I
R r r R r

  
 
  
(for helping condition)
where, I= Current flowing through the external resistance R connected across the series connection.
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57
Equivalent emf
eq 1 2
    
Equivalent internal resistance
eq 1 2
r r r 
19. Parallel Connection of cells: When n cells of equal emf E and internal resistance r are connected in
series in helping condition.
 
1 2
1 2 1 2 2 1
1 2 1 2
1 2
r r r r
I
R R
R r r r r
1
r r
 

  
 
 
 
 
 
1 2 2 1
eq
1 2
1 2
eq
1 2
r r
r r
I
r r
R r
R
r r
  


  



Equivalent emf
1 2 2 1
eq
1 2
r r
r r
  
 

Equivalent internal resistance
1 2
eq
1 2
r r
r
r r


(1) Series grouping: In series grouping of one cell is connected to cathode of other cell and so on, If
n identical cells are connected in series.
(i) Equivalent emf of the combination
eq
E nE
(ii) Equivalent internal resistance r
eq
= nr
(iii) main current = Current from each cell
nE
i
R nr
 

(iv) Potential difference across external resistance
V iR
(v) Potential difference across each cell
V
V'
n

(vi) Power dissipated in the external circuit
2
nE
R
R nr
 

 

 
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58
(vii) Condition for maximum power
2
max
E
: R nr and P n
4r
 
 
 
 
(viii) This type of combination is used when
nr R.
(2) Parallel grouping: In parallel grouping all anodes are connected at one point and all cathodes are
connected together at other point. of n identical cells are connected in parallel.
(i) Equivalent emf
eq
E E
(ii) Equivalent internal resistance
eq
r
R
n

(iii) Main current
E
i
R r / n


(iv) Potential difference across external resistance = p.d across each cell = V= iR
(v) Current form each cell
i
i '
n

(vi) Power dissipated in the circuit
2
E
P R
R r / n
 

 

 
(vii) Condition for max. power is
2
max
r E
R and P n
n 4r
 
 
 
 
(viii) This type of combination is used when r >> nR
(3) Mixed Grouping: If n identical cells are connected in a row and such m rows are connected in
parallel as shown, then
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59
(i) Equivalent emf of the combination
eq
E nE
(ii) Equivalent internal resistance of the combination
eq
nr
r
m

(iii) main current flowing through the load
nE mnE
i
nr
mR nr
R
m
 


(iv) Potential difference across load V = iR
(v) Potential difference across each cell
V
V '
n

(vi) Current form each cell
i
i '
n

(vii) Condition for maximum power
 
2
max
nr E
R and P mn
m 4r
 
(viii) Total number of cells = mn
20. Wheatsone Bridge: For a balanced wheatstone
bridge,
P R P Q
or
Q S R S
 
For Practical circuit
1
1 2 2
P Q P
or
Q
 

  
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60
21. Potentiometer:
Current
I
R L r


  
where, r = internal resistance of battery
L = length of potentiometer wire
 
resistance per unit length of potentiometer wire
L 
resistance of potentiometer wire
 
emf of battery
R = resistance connected in series

Potential difference between two points on wire separated by distance

will be,
V I ( )
R L r
 

  
 
 
 

 

Potential gardient on wire will be

, where
1
V
OR
R L r

    
  


(i) If the length of a Potentiometer wire required to balance the cell of emf
1
 is
1

, then
1 1
 
(ii) If the length of a potentiometer wire required to balance the cell of emf
2
 is
2

, then
2 2
 
2 2
l 1

 



22. On Passing electric current in a conductor:
Electric energy consumed = Heat enrgy generated (in joule)
2
2
V t
W VQ Vlt l Rt ,
R
    
where
V = Potential difference between two ends of a conductor
Q = electric charge
I = electric current
R = ohmic resistance
t = time in seconds
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61
23. Heat or thermal energy:
Heat (calorie) =
2
I Rt
J
, where J= Joule's constant = 4.2 J/cal
Heat or thermal energy:
H (joule) =
2
I Rt

Heat (H) per unit time  I
2
24. Electric power (or electrical energy consumed in unit time):
2
2
W V
P VI I R
t R
   
2
P I  
(Joule's Law)
25. Star (Y) Delta () arrangment: Here three ressistances Ra, Rb, Rc are replaced by R
1
R
2
and R
3
as
shown, then
1
RaRc
R
Ra Rb Rc

 
2
RaRb
R
Ra Rb Rc

 
3
RbRc
R
Ra Rb Rc

 
Page 8
62
Current Electricity
Page 9
63
Question
For the answer of the following questions choose the correct alternative from among the
given ones.
1. Two wires of equal lenghts, equal diameters and having resistivities 
1
and 
2
are connected in series
The equivalent resistivity of the combination is....
(A)
1 2
( )   (B)
1 2
1
( )
2
  
(C)
1 2
1
2
ρ ρ
(ρ + ρ )
(D)
2
1
ρ ρ
2. In the circuit shown in fig, current I
2
= 0 The value of E is....
(A) 3V (B) 6V
(C) 9V (D) 12V
3. In the circuit shown in fig, the reading of ammetre is....
(A) 1A (B) 2A
(C) 3A (D) 4A
4. In Fig, the galvanometer shows no deflection. what is the
resigtance X?
(A) 7 (B) 14
(C) 21 (D) 28
5. Figure, shows a network of eight resistors numbered 1 To 8, each
equal to
2
, connected to a 3V battry of negligible internal resistance
The current I in the circuit is....
(A) 0.25A (B) 0.5A
(C) 0.75A (D) 1.0 A
6.
Seven resistors, each of resistance 5
, are connected as shown in
fig, The equiualent resistance between points A and B is....
(A)
1
(B)
7
(C)
35
(D)
49
7. Figure, shows a network of seven resistors number 1 to 7, each
equal to
3
1 connecteal to a 4 V battery of negligible internal
resistance The current I in the circuit is....
(A) 0.5A (B) 1.5A
(C) 2.0A (D) 3.5A
Page 10

Current Electricity Importabt Notes and MCQs

Current Electricity Importabt Notes and MCQs

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