Question

In the circuit shown here, what is the value of the unknown resistance $R$ so that the equivalent resistance of the circuit between points $\text{P}$ and $\text{Q}$ is also equal to $R$ : -

• A. $3\Omega$
• B. $\sqrt{39}\Omega$
• C. $\sqrt{69}\Omega$
• D. $10\Omega$

Answer 1

The correct option is C $\sqrt{69}\Omega$


The equivalent resistance between points $\text{P}$ and $\text{Q}$ will be

$R=3+\frac{10(R+3)}{10+(R+3)}(\text{given,}{R}_{eq}=R)$

$R=\frac{39+3R+10R+30}{13+R}$

$13R+R^2=69+13R\Rightarrow R^2=69$

$R=\pm \sqrt{69}\Omega$

Since, resistance can not be negative

$\therefore R=\sqrt{69}\Omega$

Why this question ? It improves the skill for solving equivalent resistance of the circuit.