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Q.1. A cylindrical wire of radius a and length L is lying ——e
along the x-axis as shown in the figure. The resistivity %
of the wire varies as p(x) = pp (1+ x/21) where p,is a fa—. 6 el
constant, A potential difference of V is applied between on
the ends of the wire. tye
5 a) What is the resistance dR of the wire segment of very short
length dx, at the position x, in terms of A, x, a, L and dx?
dk = pcx) dif,
dR= §, (t+ a),
C, b) Calculate the resistance of the whole wire in terms of pp, a and L.
2 L
a= (da
8 L
= 8: ( 2 }
= 1+ A.
we ( “40 ds
>
= % $b
& Tar
% EL
& rar |
2 c) Calculate the current passing through the wire in terms of V, p,, a, and L.
tev.
R hb
6 Tat
=o vra 2 Vee
>= +S,
FB -
3 d) Calculate the current density in the wire in terms of V, p,, and L.
42
&
_ Vv
L
WS. bV/ar8,
4 c) Calculate the electric field in the wire at the point where x = L/3, in terms of V and 1.
Ea) = $ux)]
Esty) = % (4 fu. bv
o L.
\§ 4L 8, 14 Woy L
$
Q.2 Directions of the currents and the numerical values 9x5
of emf and resistances of the muiltiloop cureuit are
Biven on the figure. 5
a) Write down the loop equation for the loop |.
ABEFA (Use the numerical values of emf’s and
resistances). vt :
-é +e te ET, no
Hab E440, 20 : a8 ably e420
b) Write down the loop equation for the loop BCDEB. (Use the numerical values of emnés and
resistances).
6-4-4 - hee?
2-2%,-60, 20°
2-22%,-6R20
¢) Write down the junction equation for the junction E. (In terms of currents 1),1,,b).
Zrlye Ty
Lert of,
d) Calculate the currents 1), i, and Is.
-6
~W + 624 4¢0,-Ty)=9 Zio tt e tA
Zz
fF alot, 42; sa
Ee T-Fy ae t- C2] 3A
-4 Sax tance eats
cetez tance
ee 4-fA Eriad
am Zye ZA
e) Calculate the potential difference V, — Vp, between the points A and D.
Wovy = 20, ~ 4:03 a 443 (x ln2) = el oe GV
ar
y~ Y, (82 we LD, By 18 te l(-2)ef = tev
A oF ee 4V
f} Calculate the total power dissipated as heat in the resistors of the circuit.
Ps La, 7 bbw A, = Tey 4H
P,2 Faye ow Pie Dj a,2 Aw
, o ‘ uu Po Saw
fez Sow
g) Calculate the total power delivered by the batteries. Is the energy conservation satisfied?
A= TE, =a o FEW trupplyi'ng )
Bw HIE LE, 4M babeor bing )
Pu Sow
