If each resistance r , is along the 12 edges of a cubical skeleton of uniform wires, then find the equivalent resistance between X and Y , where X and Y are the midpoints of two opposite edges of a face of the cube.

Question

If each resistance r , is along the 12 edges of a cubical skeleton of uniform wires, then find the equivalent resistance between X and Y , where X and Y are the midpoints of two opposite edges of a face of the cube. <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-5e7tcci8jdzo.png" /> (A) (7 r/8) (B) (r/2) (C) (4 r/5) (D) (7 r/5)

Tardigrade Admin · Accepted Answer

Potential of point D and E and H and C are same. Hence, <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-5e7tcci84pe2.png" /> Re q=((3 r/4) + (r/2) + (r/2)/2)=(7 r/8)

Q. If each resistance $r$ , is along the $12$ edges of a cubical skeleton of uniform wires, then find the equivalent resistance between $X$ and $Y$ , where $X$ and $Y$ are the midpoints of two opposite edges of a face of the cube.

$\frac{7 r}{8}$

$\frac{r}{2}$

$\frac{4 r}{5}$

$\frac{7 r}{5}$

Potential of point $D$ and $E$ and $H$ and $C$ are same. Hence,

$R_{e q} = \frac{\frac{3 r}{4} + \frac{r}{2} + \frac{r}{2}}{2} = \frac{7 r}{8}$

Q. If each resistance r , is along the 12 edges of a cubical skeleton of uniform wires, then find the equivalent resistance between X and Y , where X and Y are the midpoints of two opposite edges of a face of the cube.

87r​

2r​

54r​

57r​