Twelve wires of equal length and same cross-s | vedclass

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

Question

(C) To find the equivalent resistance between two diagonally opposite corners of a cube,we can use the symmetry of the circuit.Let the current $I$ ent

Vedclass · Accepted Answer

$\frac{5}{6}R$

Vedclass · Answer

(C) To find the equivalent resistance between two diagonally opposite corners of a cube,we can use the symmetry of the circuit.Let the current $I$ enter at corner $A$ and leave at corner $D$.At node $A$,the current splits equally into $3$ branches,each with resistance $R$. The equivalent resistance of these $3$ parallel resistors is $R/3$.From these $3$ nodes,the current further splits into $6$ branches,each with resistance $R$. The equivalent resistance of these $6$ parallel resistors is $R/6$.Finally,the current converges through $3$ branches,each with resistance $R$,connected to the exit node $D$. The equivalent resistance of these $3$ parallel resistors is $R/3$.Since these three sets of resistors are in series,the total effective resistance $R_{eq}$ is:$R_{eq} = \frac{R}{3} + \frac{R}{6} + \frac{R}{3} = \frac{2R + R + 2R}{6} = \frac{5R}{6}$

Twelve wires of equal length and same cross-section are connected in the form of a cube. If the resistance of each of the wires is $R$,then the effective resistance between the two diagonal ends would be

Similar Questions

$A$ technician has only two resistance coils. By using them singly, in series or in parallel, he is able to obtain the resistances $3, 4, 12$ and $16 \, \Omega$. The resistances of the two coils are ........... $\Omega$.

$A$ student has $10$ resistors of resistance $r$. The minimum resistance made by him from given resistors is

Two resistors of resistances $2 \Omega$ and $6 \Omega$ are connected in parallel. This combination is then connected to a battery of emf $2 \text{ V}$ and internal resistance $0.5 \Omega$. What is the current flowing through the battery?

$A$ wire of length $l$ and resistance $100 \Omega$ is divided into $10$ equal parts. The first $5$ parts are connected in series while the next $5$ parts are connected in parallel. The two combinations are again connected in series. The resistance of this final combination is: (in $\Omega$)

In the given network,the equivalent resistance between $A$ and $B$ is .............. $\Omega$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module