Question

A frame of cube is made by wires each of resistance $r$, then the resistance across the body diagonal of the cube will be

• A. $\frac{3r}{4}$
  
• B. $\frac{5r}{6}$
  
• C. $\frac{7r}{12}$
  
• D. $\frac{6r}{5}$

Answer 1

The correct option is B $\frac{5r}{6}$


Let us connect an external battery of potential difference $V$ across one of the body diagonals $(1-7)$ as shown in the figure below.

Now, by symmetry the current distribution can be drawn as shown below.
In loop $12371$, applying $\text{KVL}$

$V=2Ir+Ir+2Ir=5Ir$

$R_{eq}=\frac{V}{6I}=\frac{5r}{6}$

Why this Question ? Note: $R_{eq}$ across given terminals can always be found by connecting an external battery across those terminals. $R_{eq}=\frac{V}{I}$ Tip: We can solve the above problem alternatively by redrawing the circuit by observing equipotential points in the circuit.