Answer :

Given,


The capacitance C should be equal to the equivalent capacitance.


Since the arrangement is an infinite series, addition or deletion of the repetiting components which is the 2 μF, 4 μF capacitor combinations) would not make any effect on the overall capacitance.



Hence, for simplification, we represent it as shown below,


In the figure , C in μF) represents the capacitance that gives the same value for equivalent capacitance to the infinite ladder even after it is terminated at the end. So that C and 4 μF are in series, and these are parallel to 2μF.


In this case, the effective capacitance Ceff



Which is equals to C itself, since C should not alter the effective capacitance.


So,


Or,



Or,



Or,



Or,




Since capacitance value cannot be negative, we neglect C=-2μF. Hence the equivalent capacitance of the infinite ladder is 4μF.


So, the value of capacitance that should be assigned with the terminating capacitor is 4 μF.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

In the circuit shPhysics - Exemplar

Convince yourselfHC Verma - Concepts of Physics Part 2

Each capacitor inHC Verma - Concepts of Physics Part 2

Each capacitor shHC Verma - Concepts of Physics Part 2

A cylindrical capHC Verma - Concepts of Physics Part 2

In the circuit shPhysics - Exemplar

A capacitor is maHC Verma - Concepts of Physics Part 2

Find the equivaleHC Verma - Concepts of Physics Part 2

A capacitor of caHC Verma - Concepts of Physics Part 2

A finite ladder iHC Verma - Concepts of Physics Part 2