Question

If a wire of resistance ''r'' if divided into four parts and the divided parts are placed paralel to each other than total resistance of this combination will be

Answer 1

Answer:

R = ρ×L/A

R₁ = R

R₂ = R/4

1/R₃ = 1(R/4) + 1(R/4) + 1(R/4) + 1(R/4)

1/R₃ = 16/R

R₃ = R/16

Answer 2

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We know,

When a resistance is divided into n identical resistances, each of resistanc (say R') become $\frac{</em></strong><strong><em>R</em></strong><strong><em>'</em></strong><strong><em>}</em></strong><strong><em>{N}$.

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When n identical resistors each of resistance R', are connected in parallel, the equivalent resistance is $\frac{R}{N}$.

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The resistor R, when divided into 4 parts becomes resistors of resistance $\frac{R}{4}$ each.

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The recombination of 4 resistors, each of resistance $\frac{R}{4}$ , gives a resistor of

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equivalent resistance R' of value $\frac{R}{4 } × 4$ = $\frac{R}{16}$

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Hence,

$\frac{R′}{</em></strong><strong><em>R</em></strong><strong><em>}</em></strong><strong><em>$ = $\frac{1}{16}$