Question

For the network of resistance shown in the figure the equivalent resistance of the network between the points $A$ and $B$ is $18ohm$. The value of unknown resistance $R$ is :-

• A. $8\Omega$
• B. $10\Omega$
• C. $16\Omega$
• D. $24\Omega$

Answer 1

The correct option is C $16\Omega$

The equivalent circuit is shown in figure.
here, $R_{eq1}=\frac{10\times 10}{10+10}=5\Omega$, $R_{eq2}=5+10=15\Omega$,
$R_{eq3}=\frac{15\times 10}{15+10}=6\Omega$
Thus, $R_{AB}=R||(10+6)+10=\frac{16R}{16+R}+10$
or $18=\frac{16R}{16+R}+10$
or $8=\frac{16R}{16+R}$
or $16+R=2R\Rightarrow R=16\Omega$