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A Rectangular block of iron has dimensions (1.2cm*1.2cm*15cm).Compute the resistance of the block 
a)between the two square ends
b)between the two opposite rectangular faces.
The specific resistance if iron at room temperature is (9.68*10^-8)ohm-meter.
 
 
ANS IS
a)100 micro ohm
b)0.65 micro ohm 

Asked by neeraj.unnao 1st June 2017, 4:46 PM
Answered by Expert
Answer:
begin mathsize 12px style The space resistivity space of space iron space at space room space temperature space is space 9.68 cross times 10 to the power of negative 8 end exponent space straight capital omega. straight m. space
For space the space first space case space cross minus sectional space area space of space rectangular space block space is space square equals space left parenthesis 1.2 cross times 10 to the power of negative 2 end exponent straight m right parenthesis squared space equals space space 1.44 cross times 10 to the power of negative 4 end exponent space straight m squared. space
From space equation space of space resitance comma space we space know space that space
straight R space equals space fraction numerator space ρL over denominator straight A end fraction
space space space equals fraction numerator space left parenthesis 9.68 cross times 10 to the power of negative 8 end exponent space straight capital omega. straight m right parenthesis space cross times space left parenthesis 0.15 space straight m right parenthesis over denominator 1.44 cross times 10 to the power of negative 4 end exponent space straight m squared end fraction space space
space space space equals 1.0 cross times 10 to the power of negative 4 end exponent space straight capital omega space space
space space space equals space 100 space μΩ space space
Therefore comma space the space resistance space of space the space block space measured space between space the space two space square space ends space would space be space 100 space μΩ. space space
For space the space second space case space cross minus sectional space area space of space rectangular space block space is space rectangular colon space equals space space 1.2 cross times 10 to the power of negative 2 end exponent straight m space cross times space 0.15 space straight m space equals space 1.80 cross times 10 to the power of negative 3 end exponent space straight m squared. space
We space use space the space rlation colon
straight R space equals space fraction numerator space ρL over denominator straight A end fraction
space space space space equals space fraction numerator 9.68 cross times 10 to the power of negative 8 end exponent space straight capital omega. straight m space cross times space 1.2 cross times 10 to the power of negative 2 end exponent straight m over denominator 1.80 cross times 10 to the power of negative 3 end exponent space straight m squared end fraction
space space space space equals space 6.5 cross times 10 to the power of negative 7 end exponent straight capital omega space space
space space space space space equals space 0.65 space μΩ space space
From space the space above space observation space we space conclude space that comma space the space resistance space between space two space opposite space rectangular space faces space would space be space 0.65 space μΩ. end style
Answered by Expert 2nd June 2017, 11:04 AM
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