If the resistance of each edge of a cube-shap | vedclass

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

Question

(A) To find the equivalent resistance between points $1$ and $7$ (which are diagonally opposite corners of the cube),we consider a total current $I$ e

Vedclass · Accepted Answer

$\frac{5 R}{6}$

Vedclass · Answer

(A) To find the equivalent resistance between points $1$ and $7$ (which are diagonally opposite corners of the cube),we consider a total current $I$ entering at point $1$ and leaving at point $7$.By symmetry,the current $I$ splits into three equal parts of $I/3$ at point $1$,flowing through the three edges connected to it.At the next set of nodes,these currents further split. Following the path along any edge,the current distribution is as shown in the figure.Applying Kirchhoff's loop rule along a path from $1$ to $7$ (e.g.,$1 \rightarrow 4 \rightarrow 8 \rightarrow 7$):$V = V_1 - V_7 = I_1 R_1 + I_2 R_2 + I_3 R_3$$V = (I/3)R + (I/6)R + (I/3)R$$V = I R (1/3 + 1/6 + 1/3) = I R (2/6 + 1/6 + 2/6) = I R (5/6)$Since $V = I R_{eq}$,we have $I R_{eq} = I R (5/6)$.Therefore,the equivalent resistance is $R_{eq} = \frac{5}{6} R$.

If the resistance of each edge of a cube-shaped wire frame as shown in the figure below is $R$,then the resistance between points $1$ and $7$ is

Similar Questions

For the circuit shown in the figure,the power delivered by the battery is ................ $W$.

The effective resistance between points $P$ and $Q$ of the electrical circuit shown in the figure is

When a wire of uniform cross-section $a$,length $l$ and resistance $R$ is bent into a complete circle,what is the resistance between any two diametrically opposite points?

When connected across the terminals of a cell,a voltmeter measures $5\,V$ and a connected ammeter measures $10\,A$ of current. $A$ resistance of $2\,\Omega$ is connected across the terminals of the cell. The current flowing through this resistance will be ............ $A$.

The three resistances $A, B$ and $C$ have values $3R, 6R$ and $R$ respectively. When some potential difference is applied across the network,the thermal powers dissipated by $A, B$ and $C$ are in the ratio

Vedclass Test Series

Exam Paper Generator

Online Exam Module