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2 metallic corces A and 8 of same material croeconnected inParallel arte A has length Landradius oo andB has length at and radius acompute the catio of total pesistance of pcroallelcombination andthe resistance of culte A​

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The electrical resistance of a uniform conductor is given in terms of resistivity by:

R=  

a

ρl

​  

 

where l is the length of the conductor in SI units of meters,  

a is the cross-sectional area (for a round wire a=πr  

2

 if r is radius) in units of meters squared, and ρ is the resistivity in units of ohm·meters.

∴R  

A

​  

=  

πr  

2

 

ρl

​  

 and R  

B

​  

=  

πr  

2

 

2lρ

​  

 

Resistance in parallel will be

R  

eq

​  

 

1

​  

=  

R  

A

​  

 

1

​  

+  

R  

B

​  

 

1

​  

=  

ρl

πr  

2

 

​  

+  

2lρ

πr  

2

 

​  

=  

ρ2l

3πr  

2

 

​  

 

∴R  

eq

​  

=  

3πr  

2

 

2ρl

​  

 

Now the ratio between total resistance and reistance of wire A is

R  

A

​  

 

R  

eq

​  

 

​  

=  

πr  

2

 

ρl

​  

 

3πr  

2

 

2ρl

​  

 

​  

=  

3

2

​  

389
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