The total resistance between x and y is ..... | vedclass

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

Question

(C) Let the central node be $O$. The circuit consists of four resistors connected between $x$ and $O$,and $y$ and $O$. Specifically,the resistors $8\,

Vedclass · Accepted Answer

$(4 / 3)\, \Omega$

Vedclass · Answer

(C) Let the central node be $O$. The circuit consists of four resistors connected between $x$ and $O$,and $y$ and $O$. Specifically,the resistors $8\, \Omega$ and $2\, \Omega$ are connected in parallel between $x$ and $O$. Their equivalent resistance $R_1$ is given by $1/R_1 = 1/8 + 1/2 = 5/8$,so $R_1 = 1.6\, \Omega$. The resistors $4\, \Omega$ and $6\, \Omega$ are connected in parallel between $y$ and $O$. Their equivalent resistance $R_2$ is given by $1/R_2 = 1/4 + 1/6 = 5/12$,so $R_2 = 2.4\, \Omega$. Now,the resistors $4\, \Omega$ (top) and $4\, \Omega$ (bottom) are connected in parallel between $x$ and $y$. Their equivalent resistance $R_3$ is $4/2 = 2\, \Omega$. However,looking at the circuit,the path $x-O$ and $O-y$ are in series. $R_{xOy} = R_1 + R_2 = 1.6 + 2.4 = 4\, \Omega$. Finally,this $R_{xOy}$ is in parallel with the $4\, \Omega$ resistor connected directly between $x$ and $y$. $1/R_{xy} = 1/4 + 1/4 = 2/4 = 1/2$. Therefore,$R_{xy} = 2\, \Omega$. Wait,re-evaluating the circuit: The top $4\, \Omega$ and bottom $4\, \Omega$ are in parallel with the series combination of $(8||2)$ and $(4||6)$. $R_{xy} = (4 || 4) || ( (8||2) + (4||6) ) = 2 || (1.6 + 2.4) = 2 || 4 = (2 	imes 4) / (2 + 4) = 8 / 6 = 4/3\, \Omega$.

The total resistance between $x$ and $y$ is ...... $\Omega$.

Similar Questions

$A$ conductor of resistance $3 \Omega$ is stretched uniformly until its length is doubled. The wire is now bent in the form of an equilateral triangle. The effective resistance between the ends of any side of the triangle in ohms is

Resistors of $4\, R, 16\, R, 64\, R, \dots \infty$ are connected in series. Find their equivalent resistance.

$A$ wire of resistance $9 \ \Omega$ is bent to form an equilateral triangle. Then the equivalent resistance across any two vertices will be . . . . . . ohm.

What is series connection of resistors,and what is parallel connection of resistors?

Vedclass Test Series

Exam Paper Generator

Online Exam Module