JEE Physics/ Lakshmikanta Satapathy/ Direct Current QA part 14/ JEE question on comparison of Voltage Power Current density and Electric field of two wires in series solved with the related concepts

1. Physics Helpline
L K Satapathy
Direct Current - 14
Voltage / Current Density
Power / Electric Field
Comparison of

2. Physics Helpline
L K Satapathy
Direct Current - 14
Cells in Parallel
Question : Two wires AB and BC, each of length L , and made of the same
material are joined together as shown in the figure.
(a) PD across BC is twice that across AB
(b) Power dissipated in BC is four times that in AB
(c) Current densities in AB and BC are equal
(d) Electric field inside AB and BC are equal
A B C
L L
I
The radius of wire AB is twice the radius of wire BC. If current I flows through
the composite wire , then

3. Physics Helpline
L K Satapathy
Direct Current - 14
Cells in Parallel
CONCEPTS
In SERIES , currents through both resistors are same
POWER Dissipated 2
.P I R P R  
Potential Difference .V I R V R  
Resistance
2 2
. . 1
.
L L
R R
A r r
 

   
Current Density
2 2
1
.
I I
J J
A r r
   
Electric field
V
E E V
L
  
2R1R
V
2P1P
2V1V
I
[ I = const.]
[ I = const.]
[ I = const.]
[ L = const.]
[ L = const.]

4. Physics Helpline
L K Satapathy
Direct Current - 14
Cells in Parallel
Given :
Wires AB and BC are made of same material 1 2    
Radius of AB = 2 (Radius of BC) 1 22r r 
Area of cross section of AB = 4(Area of cross section of BC) 1 24A A 
Lengths of AB and BC are equal 1 2L L L  
Resistances
2
21
1 2
1 2 1
. . 1
4
ARL L
R and R
A A R A
 
    
A B C
L L
I

5. Physics Helpline
L K Satapathy
Direct Current - 14
Cells in Parallel
(d) E inside AB and BC are equal
(a) P D across BC is twice across AB
(b) Power in BC is four times that in AB
(c) J in AB and BC are equal
1 1
2 1
2 2
1
4
4
V R
V V
V R
   
1 1
2 1
2 2
1
4
4
P R
P P
P R
   
1 2
2 1
2 1
1
4
4
J A
J J
J A
   
1 1
2 1
2 2
1
4
4
E V
E E
E V
   
Correct option = (b)
Answer : We test the options for correctness

6. Physics Helpline
L K Satapathy
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