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

What will be the equivalent resistance of the circuit between $x$ and $y$?

In the given circuit,the current through $2 \ \Omega$ resistor is

For the circuit shown,the value of current at time $t=3.2 \, s$ will be ...... $A$. (Voltage distribution $V(t)$ is shown by Figure $1$ and the circuit is shown in Figure $2$)

The magnitude of $i$ in ampere unit is

$A$ battery of internal resistance $4 \, \Omega$ is connected to the network of resistors as shown. In order for the maximum power to be delivered to the network, the value of $R$ in $\Omega$ should be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module