Question

A battery of $10 \,V$ 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. $3 R$
• D. $12 R$

Answer 1

Answer: (A)

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

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