Current Electricity Question 22
Question 22 - 01 February - Shift 2
Equivalent resistance between the adjacent corners of a regular n-sided polygon of uniform wire of resistance $R$ would be:
(1) $\frac{(n-1) R}{n^{2}}$
(2) $\frac{(n-1) R}{(2 n-1)}$
(3) $\frac{n^{2} R}{n-1}$
(4) $\frac{(n-1) R}{n}$
Show Answer
Answer: (1)
Solution:
Formula: Combination of Resistances
Suppose resistance of each arm is $r$, then $r=R / n$
$R _{\text{eq }(A B)}=\frac{R_1 R_2}{R_1+R_2}$
$\frac{r(n-1) r}{r+(n-1) r}$
$=\frac{r(n-1) r}{n r}$
$=\frac{n-1}{n} r$
$=\frac{(n-1) R}{n^{2}}$
