Question

A piece of wire of resistance $R$ is cut into five equal parts out of which four of them are connected to forms a square $ABCD$. The fifth one is connected diagonally across $BD$. If a battery is connected across $AC$, what would be the equivalent resistance in the circuit?

• A. $R/25$
• B. $4R/5$
• C. $R/5$
• D. $2R/5$

Answer 1

The correct option is C $R/5$

According to the diagram:
Let resistance of each part be '$r$', $r=\frac{R}{5}$
As circuit is forming wheat stone bridge, so
$R_{eq}=[R_{AD}+R_{DC}]\parallel [R_{AB}+R_{BC}]$
$=[\frac{R}{5}+\frac{R}{5}]\parallel [\frac{R}{5}+\frac{R}{5}]=\left[\frac{2R}{5}\right]\parallel \left[\frac{2R}{5}\right]$
As both resistance $\frac{2R}{5}$ in parallel. So $R_{eq}$ will be equal to $\frac{R}{5}$