A ring is made of a wire having a total resis | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the resistances of the two segments of the ring be $R_1$ and $R_2$. Since the segments are in parallel,the equivalent resistance $R$ is given

Vedclass · Accepted Answer

$\frac{l_1}{l_2} = \frac{1}{2}$

Vedclass · Answer

(B) Let the resistances of the two segments of the ring be $R_1$ and $R_2$. Since the segments are in parallel,the equivalent resistance $R$ is given by:$\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} \Rightarrow R = \frac{R_1 R_2}{R_1 + R_2} = \frac{8}{3}\,\Omega$.Given the total resistance $R_0 = R_1 + R_2 = 12\,\Omega$,we have:$R_1 R_2 = \frac{8}{3} 	imes 12 = 32$.Now,we use the identity $(R_2 - R_1)^2 = (R_1 + R_2)^2 - 4R_1 R_2$:$(R_2 - R_1)^2 = 12^2 - 4(32) = 144 - 128 = 16$.Thus,$R_2 - R_1 = 4\,\Omega$.Solving the system $R_1 + R_2 = 12$ and $R_2 - R_1 = 4$,we get $2R_2 = 16 \Rightarrow R_2 = 8\,\Omega$ and $R_1 = 4\,\Omega$.Since resistance is proportional to length $(R \propto l)$,the ratio of lengths is $\frac{l_1}{l_2} = \frac{R_1}{R_2} = \frac{4}{8} = \frac{1}{2}$.

Similar Questions

$A$ wire has a resistance of $12 \, \Omega$. It is bent in the form of an equilateral triangle. The effective resistance between any two corners of the triangle is

Three resistances of $1\, \Omega$ each are connected in parallel. Such a connection is then connected in series with a $\frac{2}{3}\, \Omega$ resistor. The resultant resistance will be ........... $\Omega$.

The resistance of the series combination of two identical resistors is $S$. When they are joined in parallel,the total resistance is $P$. If $S = nP$,then the minimum possible value of $n$ is

You are given $n$ resistors each of resistance $r$. They are first connected to get the minimum possible resistance. In the second case,they are again connected differently to get the maximum possible resistance. Calculate the ratio between minimum and maximum values of resistance so obtained.

$10$ resistors,each of resistance $10\,\Omega$,can be connected to obtain maximum and minimum equivalent resistance. The ratio of maximum to minimum equivalent resistance will be $..........$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module