Equivalent resistance between the adjacent corners of a regular -sided polygon of uniform wire of resistance would be [2023]

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Q.
Equivalent resistance between the adjacent corners of a regular $n$ -sided polygon of uniform wire of resistance $R$ would be [2023]

1 $\frac{(n - 1) R}{n^{2}}$

2 $\frac{(n - 1) R}{(2 n - 1)}$

3 $\frac{n^{2} R}{(n - 1)}$

4 $\frac{(n - 1) R}{n}$

Ans.
(1)

$Suppose resistance of each arm is r, then r = \frac{R}{n}$

$R_{eq} (A B) = \frac{R_{1} R_{2}}{R_{1} + R_{2}}$

$= \frac{r (n - 1) r}{r + (n - 1) r} = \frac{r (n - 1) r}{n r} = \frac{n - 1}{n} r = \frac{(n - 1) R}{n^{2}}$

Solution

Q.
Equivalent resistance between the adjacent corners of a regular $n$ -sided polygon of uniform wire of resistance $R$ would be [2023]

1 $\frac{(n - 1) R}{n^{2}}$

2 $\frac{(n - 1) R}{(2 n - 1)}$

3 $\frac{n^{2} R}{(n - 1)}$

4 $\frac{(n - 1) R}{n}$

Ans.
(1)

$Suppose resistance of each arm is r, then r = \frac{R}{n}$

$R_{eq} (A B) = \frac{R_{1} R_{2}}{R_{1} + R_{2}}$

$= \frac{r (n - 1) r}{r + (n - 1) r} = \frac{r (n - 1) r}{n r} = \frac{n - 1}{n} r = \frac{(n - 1) R}{n^{2}}$

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Solution

Q. Equivalent resistance between the adjacent corners of a regular n-sided polygon of uniform wire of resistance R would be [2023]

1 (n-1)Rn2

2 (n-1)R(2n-1)

3 n2R(n-1)

4 (n-1)Rn

Ans. (1) Suppose resistance of each arm is r, then r=Rn Req(AB)=R1R2R1+R2 =r(n-1)rr+(n-1)r=r(n-1)rnr=n-1nr=(n-1)Rn2

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Q.
Equivalent resistance between the adjacent corners of a regular $n$ -sided polygon of uniform wire of resistance $R$ would be [2023]

1 $\frac{(n - 1) R}{n^{2}}$

2 $\frac{(n - 1) R}{(2 n - 1)}$

3 $\frac{n^{2} R}{(n - 1)}$

4 $\frac{(n - 1) R}{n}$

Ans.
(1)

$Suppose resistance of each arm is r, then r = \frac{R}{n}$

$R_{eq} (A B) = \frac{R_{1} R_{2}}{R_{1} + R_{2}}$

$= \frac{r (n - 1) r}{r + (n - 1) r} = \frac{r (n - 1) r}{n r} = \frac{n - 1}{n} r = \frac{(n - 1) R}{n^{2}}$