Question

7. a piece of wire of resistance R is cut into five
equal parts. These parts are then connected in
parallel, if the equivalent resistance of this
combination is R', then the ratio R/ R' is

​

Answer 1

Answer:

Explanation:

ANSWER

We know,

1.When a resistance is divided into n identical resistances, each of resistance (say R') become  

n

R

​  

.

2.When n identical resistors each of resistance R', are connected in parallel, the equivalent resistance is  

n

R  

′

 

​  

 

The resistor R ,when divided into five parts become resistors of resistance  

5

R

​  

each.

The recombination of five resistors, each of resistance    

5

R

​  

, gives a resistor of equivalent resistance R' of value  

5

5

R

​  

 

​  

=  

25

R

​  

 

Hence,

R  

′

 

R

​  

=  

1

25

​

Answer 2

Let the length of resistance R be L

Let the resistance of each part after cutting be R

s

Since resistance is proportional to the length of the resistor,

R

s

=R/5.....................(i)

For resistors in parallel,

R

′

1

=

R

1

1

+

R

2

1

+

R

3

1

+

R

4

1

+

R

5

1

⟹R

′

=R

s

/5................(ii)

From (i) and (ii),

R

′

=R/25

R/R

′

=25

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