2019-03-01_Physics_Times

After connecting E, the current through 8 is

1 1

I A E A 8 0 E 4V

2 2

      

After the switch  is closed at t = 0 the inductor

does not allow the current through it and hence

bulb B 2 glows first. After long time the inductor

behaves like a conductor and hence resistance of

the upper wire is less and current through B 1 is

more.

Efficiency,

Output power

Input power



80 200

16

100 4000

s s s

s

p p

V I I

I A

V I





     

Also,

4000

4000 40

p p p 100

V I   I  A

After closing the switch the net potential of the

sphere is zero as it is connected to earth. The

electric field inside the shell is zero (Gauss law)

and hence the potential inside the shell is constant

every where inside the shell and also zero at the

centre.

The net potential at O is

0

(^4040)
o
q q
V
x R
 
Where q is the net charge on the sphere. By
differentiating the equation w.r.t to
0
2
0 0
0
4 4
q dx dq / dt
x dt R

 
0
2
dq Rq dx
.
dt x dt

The current 20
Rq
i v
x

dx dq
v ,i
dt dt
 
   
 
In steady state, the net outward heat flow is
constant, and does not depend on radial position.
Let
2
1 (4 )
dT
c i K r
dr
   
1
4 2
dT c
dr Kr
  

0
1
2 2
1
4
T r
T a
c
dT dr
K r
 

  

1

0

1 1

2

4

c

T T

K r a

 

    

   (1)

When r a   2 T T 0

1

0 0

1 1

2

4 2

c

T T

K a a

    

   (2)

From eq’s (1) & (2) we get

(^40) at 3
3 2
T a
T r
2
1
1
T
T
  
Coefficient of performance
2 2 1
1 2 2 1
/ (1 ) 1
1
1 ( / )
T T T
T T T T
 
     
   
Final pressure in the containers will be the same
0 0
0 0
A B A B
A B
PV PV PV PV
RT RT RT RT
  
(^00)  
(^20000)
A B
P P P P
V V
T T T T
     
(^40)
3
P
 P
For mixture of gases,
(^1122)
1 2
V V
V
n C n C
C
n n



where ,
2
f
C R f is degree of freedom
and
(^1122)
1 2
p p
p
n C n C
C
n n



where
3.Sol:
4.Sol:
5.Sol:
6.Sol:
7.Sol:
8.Sol:
9.Sol:
1
2
p
f
C R
 
  
 
For helium, n 1  4,f 3
For oxygen, 2
1
, 5
2
n  f
5 1 7
(^447)
(^222) 1.62
3 1 5 29
4
2 2 2
p
V
R R
C
C R R
  
   
  