Current Electricity, Charging & Discharging Of Capacitors / वर्तमान बिजली, चार्ज और कैपेसिटर का निर
JEE Main & Advanced
Physics
Current Electricity, Charging & Discharging Of Capacitors / वर्तमान बिजली, चार्ज और कैपेसिटर का निर
Question Bank
Grouping of Resistances
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 \[R=\sqrt{69}\Omega \].