Equivalent resistance between the adjacent corners of a regular $n$-sided polygon of uniform wire of resistance $R$ would be:
A$\frac{(n-1) R}{n^2}$
B$\frac{(n-1) R}{(2 n-1)}$
C$\frac{n^2 R}{n-1}$
D$\frac{(n-1) R}{n}$
JEE MAIN 2023, Medium
Download our app for free and get started
A$\frac{(n-1) R}{n^2}$
a Suppose resistance of each arm is $r$, then $r = R / n$
$R _{ eq(AB )}=\frac{ R _1 R_2}{R_1+R_2}$
$\frac{ r ( n -1) r }{ r +( n -1) r }$
$=\frac{ r ( n -1) r }{ nr }$
$=\frac{ n -1}{ n } r$
$=\frac{( n -1) R }{ n ^2}$
Download our app
and get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
The current through a wire depends on time as $i = (2+3t)\, mA$. The charge crossing through a section of the wire in $1\, min$ is .............. $\mathrm{C}$
A parallel combination of two resistors, of $1 \,\Omega$ each, is connected in series with a $1.5 \,\Omega$ resistor. The total combination is connected across a $10\, V$ battery. The current flowing in the circuit is .............. $A$
In the circuit shown in figure, the power which is dissipated as heat in the $6\,\Omega$ resistor is $6\,W$. What is the value of resistance $R$ in the circuit?................... $\Omega$
Four wires of the same diameter are connected in turn between two points, maintained at a constant potential difference. Their resistivities are; $\rho $ and $L$ (wire $1$ )., $1.2\,\rho $ and $1.2\,L$ (wire $2$ ), $0.9\,\rho $ and $0.9\,L$ (wire $3$ ) and $\rho $ and $1.5\,L$ (wire $4$ ). Rank the wires according to the rates at which energy is dissipated as heat, greatest first
Eight copper wire of length $l$ and diameter $d$ are joined in parallel to form a single composite conductor of resistance $R$. If a single copper wire of length $2\,l$ have the same resistance $(R)$ then its diameter will be $.....d$.
We have two wires $A$ and $B$ of same mass and same material. The diameter of the wire $A$ is half of that $B$. If the resistance of wire $A$ is $24\, ohm$ then the resistance of wire $B$ will be ................ $Ohm$