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Question

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 RR' is _____.


A

125

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B

15

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C

5

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D

25

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Solution

The correct option is D

25


Step 1. Given data

It is given that a piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel.

The equivalent resistance of the combination is R'.

Step 2: Formula used

Resistance is the opposition that an electrical device has to the flow of electrical current. It is represented by symbol R.

The formula to find the resistance is,

R=ρlA

Here, ρ is the resistivity, l is the length of wire and A is the cross sectional area.

Step 3. Find the ratio of RR'.

The resistance R is directly proportional to length of the wire.

Thus, the resistance of each five parts after cutting the wire is,

R1=R2=R3=R4=R5=R5

When all the resistances are connected in parallel,

Let us consider, R' is the equivalent resistance.

Therefore,

1R'=1R1+1R2+1R3+1R4+1R5

=1R5+1R5+1R5+1R5+1R5

=5R+5R+5R+5R+5R

R'=R25

Now, we will find the ratio of RR'.

We will find the ratio of RR'.

RR'=RR25

=25RR

=25

The ratio of RR' is 25.

Hence, option D is correct answer.


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