Question

The circuit shown has a resistor of equal resistance R.Find the equivalent resistance between A and B, when the key is closed.

• A. $\frac{11R}{12}$
• B. $\frac{13R}{12}$
• C. $\frac{R}{5}$
• D. $\frac{15R}{12}$

Answer 1

The correct option is C $\frac{R}{5}$

As from the configuration, we can deduce that, $1$ and $2$ are in parallel,

$\frac{1}{R_{12}}=\frac{1}{R}+\frac{1}{R}=\frac{2}{R}$

Now potential at $y$ will be some as potential at $\theta$, which implies that there will be no current through arm $y\theta$ and hence that's why resister $6$ can be neglected and hence then there will be five $5$ resister which are in parallel with each other.

The resultant resistance is given by

$\frac{1}{R_{eq}}=\frac{1}{R}+\frac{1}{R}+\frac{1}{R}+\frac{1}{R}+\frac{1}{R}=\frac{5}{R}$

$⟹R_{eq}=\frac{R}{5}$