A cube is formed with ten identical resistanc | 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 $A$ and $B$,we first note that the shorting wires along $AC$ and $BD$ make the potential at $A$ e

Vedclass · Accepted Answer

$\frac{R}{2}$

Vedclass · Answer

(A) To find the equivalent resistance between points $A$ and $B$,we first note that the shorting wires along $AC$ and $BD$ make the potential at $A$ equal to the potential at $C$ $(V_A = V_C)$ and the potential at $B$ equal to the potential at $D$ $(V_B = V_D)$.By collapsing the nodes $A$ and $C$ into a single node and $B$ and $D$ into another single node,we can redraw the circuit.In this configuration,the ten resistors are arranged such that they form two parallel branches,each consisting of five resistors in a series-parallel combination. Specifically,the symmetry of the cube allows us to simplify the network into two parallel paths,each having an equivalent resistance of $R$. Thus,the total equivalent resistance $R_{AB}$ is given by the parallel combination of these two paths:$R_{AB} = \frac{R 	imes R}{R + R} = \frac{R}{2} \, \Omega$.

$A$ cube is formed with ten identical resistances $R$ (thick lines) and two shorting wires (dotted lines) along the arms $AC$ and $BD$ as shown in the figure below. The resistance between point $A$ and $B$ is ........... $\Omega$.

Similar Questions

An electric heater and an electric bulb are rated $500\, W, 220\, V$ and $100\, W, 220\, V$ respectively. Both are connected in series to a $220\, V$ $a.c.$ mains. The current in the circuit when both are connected in series is ................ $A$.

The current $I_{1}$ (in $A$) flowing through the $1\; \Omega$ resistor in the following circuit is:

The equivalent resistance between $A$ and $B$ in the figure is

The equivalent resistance of a series combination of two resistors is $s$. When they are connected in parallel,the equivalent resistance is $p$. If $s = np$,then the minimum value for $n$ is (Round off to the nearest integer).

What is the equivalent resistance between $A$ and $B$ in the given circuit?

Vedclass Test Series

Exam Paper Generator

Online Exam Module