Question

1. 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:

When we cut the wire into 5 parts, each one has a length of l5 and all other parameters remain unchanged. So the resistance of each new segment isR5. Connecting them parallel gives a network as shown in fig1. So the ratio RR′=25 , which is the required answer.

Explanation:

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Answer 2

Answer:

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 -----------(1)

For resistors in parallel,

$\frac{1}{r'} = \frac{1}{r1} + \frac{1}{r2} + \frac{1}{r3} + \frac{1}{r4} + \frac{1}{r5}$

⟹ R′ =R.s /5 -------- (2)

From (i) and (ii),

R′ =R/25

R/R′ =25

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