Question

A battery of $10V$ and negligible internal resistance is connected across the diagonally opposite corners of a cubical network consisting of $12$ resistors each of resistance $1\Omega$. The equivalence resistance of the network is

• A. $\frac{5}{6}R$
• B. $\frac{6}{5}R$
• C. $3R$
• D. $12R$

Answer 1

Answer: (A)

In a closed loop, say, $ABC{C}^{\prime }EA$ and apply Kirchhoff's second rule,$-IR-\left(\frac{I}{2}\right)R-IR+\epsilon =0$

where, $R$ is the resistance of each edge and $\epsilon$ the emf of battery. Thus,
$\epsilon =\frac{5}{2}IR$
The equivalent resistance $R_{eq}$ of the network is
$R_{eq}=\frac{\epsilon }{3I}=\frac{5}{6}R$
The effective resistance between two diagonally opposite ends $=5R/6$.