question_answer

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                           [MP PET 2001]

A)         3 ohms

B)         \[\sqrt{39}\,ohms\]

C)         \[\sqrt{69}\,ohms\]

D)         10 ohms

Correct Answer: C

Solution :

                                         The given circuit can be simplified as follows \[R=3+\frac{10\times (3+R)}{10+3+R}\]\[=3+\frac{30+10R}{13+R}\] \[R=\frac{39+3R+30+10R}{13+R}=\frac{69+13R}{13+R}\]         \[13R+{{R}^{2}}=69+13R\] Þ \[R=\sqrt{69}\Omega \].