Q. In the circuit shown here, what is the value of the unknown resistor $R$ so that the total resistance of the circuit between points $P$ and $Q$ is also equal to $R$
A) $3\ ohm$
B) $\sqrt{39}\ ohm$
C) $\sqrt{69}\ ohm$
D) $10\ ohm$
Explanation
(c) The given circuit can be simplified as follows
$R = 3 + \frac{10 \times (3 + R)}{10 + 3 + R} = 3 + \frac{30 + 10R}{13 + R}$
$R = \frac{39 + 3R + 30 + 10R}{13 + R} = \frac{69 + 13R}{13 + R}$
$13R + R^{2} = 69 + 13R \Rightarrow R = \sqrt{69}\Omega$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.