The answer is given below someone show the calculation pleases?! I am stuck at this question

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1 Answer
Feb 15, 2018

See the image and explanation.

Explanation:

Given:
Thin film of nichrome with resistivity # rho =1.0 xx 10^-6 Omega m#.
Thickness of film = #1xx 10^-6 m #
Surface area = #1 mm^2# ------ constant.

To find: resistance between opposite edges of film.

(a)Shape of film = square=> area #1 mm xx 1mm #= side x side

#=># length of sheet across the edges( terminals). = 1mm

#=> l = 1 xx 10^-3 m#

Cross section area = thickness of film x width of film:

#=>A=1xx 10^-6 m xx 1mm = 1xx 10^-9m#
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#R= rho xx l/A#

# =>R = 1.0 xx 10^-6 xx (1xx 10^-3) / (1 xx 10^-9 m^2)#

#R = 1 Omega#

b) Shape of rectangle with length 20 times width.
Case 1 : terminals across longer edge:
Surface area = #1 xx 10^-6 m^2#
Given : #l= 20 xx w #

#Area= l xx w =>20 w xx w = 1xx 10^-6 m^2#

#=> 20 w^2 = 1 xx10^-6 m^2#

# w= sqrt ((1 xx10^-6 )/20)#

Now the cross sectional area will be width xx thickness:

#A =sqrt ((1 xx10^-6 )/20) xx 1 xx10^-6#

and Length across terminals:

#l = 20 w = 20 xx sqrt ((1 xx10^-6 )/20) #

#R= rho xx l/A#

#=> R = 1 xx10^-6 xx [20 xx sqrt ((1 xx10^-6 )/20)]/[sqrt ((1 xx10^-6 )/20) xx 1 xx10^-6] #

#=> R = 20 Omega#

Case 2 : terminals across shorter edge:
from case 1 : # w= sqrt ((1 xx10^-6 )/20)#
Now the cross sectional area will be length xx thickness:

#A =20w xx 1 xx10^-6#

and Length across terminals will be :

#l = w #

#R= rho xx l/A = rho xx w/ (20w xx 1 xx10^-6)#

#=> R = 1 xx10^-6 xx (sqrt ((1 xx10^-6 )/20))/[ 20 xx sqrt ((1 xx10^-6 )/20) xx 1 xx 10^-6] #

#=> R = 1/20 = 0.05 Omega#