Question

For what value of $R$, the net resistance of the circuit will be $18\Omega$?

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

Answer 1

The correct option is C $16\Omega$

Circuit can be reduced as follows


Again, simplify the circuit,


Resistance $10+6(=16)\Omega$ and $R\Omega$ are in parallel, so effective resistance between $\text{A}$ and $\text{B}$ is

$\therefore R_{AB}=10+\frac{16\times R}{16+R}$

$\Rightarrow 18=10+\frac{16R}{16+R}(\text{given},R_{AB}=18\Omega )$

$\Rightarrow 288+18R=160+10R+16R$

$\Rightarrow 8R=128$

$\therefore R=16\Omega$

Hence, option option $\left(c\right)$ is correct.