1.

A wite of given material having length land area of cross- section. A has a resistance of 4 π . What would be the resistance of another wire of the same material having length l 12 and area of cross- section 2 A?​

Answer»

Answer:

Wire of UNIFORM CROSS-section has a resistance of R. Let the DIAMETER be d,  the length of the wire be l cross-sectional area be A.

Now the resistance of a wire can be expressed as:

R=ρ  

A

l

​  

 

Where resistivity is ρ.

Now a second wire is twice as long and of half cross section.

Let final length be l  

1

​  

, diameter be d  

1

​  

 and

cross section Area be A  

1

​  

.

A  

1

​  

=  

2

A

​  

 

R  

1

​  

=ρ  

A  

1

​  

 

l  

1

​  

 

​  

 

Putting the VALUE of l  

1

​  

=2L and A  

1

​  

=  

2

A

​  

 

We have, resistance of the new second wire, R  

2

​  

=ρ  

A

4l

​  

=4×R  

1

​  

=4×8=32Ω

Explanation:


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