Search any question & find its solution
Question:
Answered & Verified by Expert
The equivalent resistance of the infinite network given below is:
Options:
Solution:
1262 Upvotes
Verified Answer
The correct answer is:
$(1+\sqrt{3}) \Omega$
Let net resistance of the given infinite network be ' \(R\) '
Now, the circuit can be modified as
Now, \(R_{\text {net }}=R=1+1+\frac{R}{R+1}\)
\(\begin{aligned}
& \therefore R=2+\frac{R}{R+1} \\
& R^2+R=2 R+2+R \\
& R^2-2 R-2=0 \\
& R=\left(\frac{2 \pm \sqrt{4+8}}{2}\right) \\
& R=(1+\sqrt{3}) \Omega
\end{aligned}\)
Now, the circuit can be modified as
Now, \(R_{\text {net }}=R=1+1+\frac{R}{R+1}\)
\(\begin{aligned}
& \therefore R=2+\frac{R}{R+1} \\
& R^2+R=2 R+2+R \\
& R^2-2 R-2=0 \\
& R=\left(\frac{2 \pm \sqrt{4+8}}{2}\right) \\
& R=(1+\sqrt{3}) \Omega
\end{aligned}\)
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.