A uniform wire of length l and having resistance R is cut into n equal parts and all parts are connected in parallel, then the equivalent resistance will be :

Question

A uniform wire of length l and having resistance R is cut into n equal parts and all parts are connected in parallel, then the equivalent resistance will be : (A)  R  (B)  R/n  (C)  R/n2 (D) n2R

Tardigrade Admin · Accepted Answer

Resistance of each part R'=(R/n) When, these parts are connected in parallel. Then, (1/R'')=(1/R')+(1/R') ldots n time =(n/R') ∴ R''=(R'/n)=(R/n2)

Q. A uniform wire of length $l$ and having resistance $R$ is cut into $n$ equal parts and all parts are connected in parallel, then the equivalent resistance will be :

$R$

$R / n$

$R / n^{2}$

$n^{2} R$

Resistance of each part $R^{'} = \frac{R}{n}$
When, these parts are connected in parallel.
Then, $\frac{1}{R ^{''}} = \frac{1}{R ^{'}} + \frac{1}{R ^{'}} \dots n$ time
$= \frac{n}{R ^{'}}$
$∴ R^{''} = \frac{R ^{'}}{n} = \frac{R}{n ^{2}}$

Q. A uniform wire of length l and having resistance R is cut into n equal parts and all parts are connected in parallel, then the equivalent resistance will be :

R

R/n

R/n2

n2R

Resistance of each part R′=nR​ When, these parts are connected in parallel. Then, R′′1​=R′1​+R′1​…n time =R′n​ ∴R′′=nR′​=n2R​

Q. A uniform wire of length $l$ and having resistance $R$ is cut into $n$ equal parts and all parts are connected in parallel, then the equivalent resistance will be :

$R$

$R / n$

$R / n^{2}$

$n^{2} R$

Resistance of each part $R^{'} = \frac{R}{n}$
When, these parts are connected in parallel.
Then, $\frac{1}{R ^{''}} = \frac{1}{R ^{'}} + \frac{1}{R ^{'}} \dots n$ time
$= \frac{n}{R ^{'}}$
$∴ R^{''} = \frac{R ^{'}}{n} = \frac{R}{n ^{2}}$